Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,21,Mod(3,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 21, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.3");
S:= CuspForms(chi, 21);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 21 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(20.2811012082\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 66008406614424 x^{16} + \cdots + 53\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{153}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.15 | ||
Root | \(-24233.2 + 2.60731e6i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.3 |
Dual form | 8.21.d.b.3.16 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 829.658 | − | 600.204i | 0.810212 | − | 0.586136i | ||||
\(3\) | −103279. | −1.74904 | −0.874519 | − | 0.484991i | \(-0.838823\pi\) | ||||
−0.874519 | + | 0.484991i | \(0.838823\pi\) | |||||||
\(4\) | 328087. | − | 995927.i | 0.312888 | − | 0.949790i | ||||
\(5\) | − | 1.04292e7i | − | 1.06796i | −0.845499 | − | 0.533978i | \(-0.820697\pi\) | ||
0.845499 | − | 0.533978i | \(-0.179303\pi\) | |||||||
\(6\) | −8.56862e7 | + | 6.19884e7i | −1.41709 | + | 1.02517i | ||||
\(7\) | − | 3.68005e8i | − | 1.30279i | −0.758740 | − | 0.651394i | \(-0.774185\pi\) | ||
0.758740 | − | 0.651394i | \(-0.225815\pi\) | |||||||
\(8\) | −3.25559e8 | − | 1.02320e9i | −0.303200 | − | 0.952927i | ||||
\(9\) | 7.17976e9 | 2.05914 | ||||||||
\(10\) | −6.25967e9 | − | 8.65271e9i | −0.625967 | − | 0.865271i | ||||
\(11\) | −3.35341e10 | −1.29289 | −0.646443 | − | 0.762962i | \(-0.723744\pi\) | ||||
−0.646443 | + | 0.762962i | \(0.723744\pi\) | |||||||
\(12\) | −3.38845e10 | + | 1.02858e11i | −0.547254 | + | 1.66122i | ||||
\(13\) | 1.95314e11i | 1.41677i | 0.705824 | + | 0.708387i | \(0.250577\pi\) | ||||
−0.705824 | + | 0.708387i | \(0.749423\pi\) | |||||||
\(14\) | −2.20878e11 | − | 3.05318e11i | −0.763611 | − | 1.05554i | ||||
\(15\) | 1.07712e12i | 1.86789i | ||||||||
\(16\) | −8.84229e11 | − | 6.53502e11i | −0.804202 | − | 0.594357i | ||||
\(17\) | −1.59958e11 | −0.0793445 | −0.0396722 | − | 0.999213i | \(-0.512631\pi\) | ||||
−0.0396722 | + | 0.999213i | \(0.512631\pi\) | |||||||
\(18\) | 5.95674e12 | − | 4.30932e12i | 1.66834 | − | 1.20693i | ||||
\(19\) | 4.90447e12 | 0.799937 | 0.399969 | − | 0.916529i | \(-0.369021\pi\) | ||||
0.399969 | + | 0.916529i | \(0.369021\pi\) | |||||||
\(20\) | −1.03868e13 | − | 3.42170e12i | −1.01433 | − | 0.334151i | ||||
\(21\) | 3.80072e13i | 2.27863i | ||||||||
\(22\) | −2.78218e13 | + | 2.01273e13i | −1.04751 | + | 0.757807i | ||||
\(23\) | − | 3.43682e13i | − | 0.829619i | −0.909908 | − | 0.414810i | \(-0.863848\pi\) | ||
0.909908 | − | 0.414810i | \(-0.136152\pi\) | |||||||
\(24\) | 3.36234e13 | + | 1.05675e14i | 0.530309 | + | 1.66671i | ||||
\(25\) | −1.34018e13 | −0.140528 | ||||||||
\(26\) | 1.17228e14 | + | 1.62044e14i | 0.830423 | + | 1.14789i | ||||
\(27\) | −3.81407e14 | −1.85247 | ||||||||
\(28\) | −3.66506e14 | − | 1.20738e14i | −1.23737 | − | 0.407627i | ||||
\(29\) | 1.07520e14i | 0.255569i | 0.991802 | + | 0.127785i | \(0.0407867\pi\) | ||||
−0.991802 | + | 0.127785i | \(0.959213\pi\) | |||||||
\(30\) | 6.46493e14 | + | 8.93643e14i | 1.09484 | + | 1.51339i | ||||
\(31\) | 3.09876e13i | 0.0378069i | 0.999821 | + | 0.0189035i | \(0.00601752\pi\) | ||||
−0.999821 | + | 0.0189035i | \(0.993982\pi\) | |||||||
\(32\) | −1.12584e15 | − | 1.14654e13i | −0.999948 | − | 0.0101833i | ||||
\(33\) | 3.46337e15 | 2.26131 | ||||||||
\(34\) | −1.32710e14 | + | 9.60073e13i | −0.0642859 | + | 0.0465067i | ||||
\(35\) | −3.83802e15 | −1.39132 | ||||||||
\(36\) | 2.35559e15 | − | 7.15052e15i | 0.644280 | − | 1.95575i | ||||
\(37\) | 4.26943e15i | 0.887876i | 0.896057 | + | 0.443938i | \(0.146419\pi\) | ||||
−0.896057 | + | 0.443938i | \(0.853581\pi\) | |||||||
\(38\) | 4.06903e15 | − | 2.94368e15i | 0.648119 | − | 0.468872i | ||||
\(39\) | − | 2.01719e16i | − | 2.47799i | ||||||
\(40\) | −1.06712e16 | + | 3.39533e15i | −1.01768 | + | 0.323804i | ||||
\(41\) | −3.78792e15 | −0.282203 | −0.141102 | − | 0.989995i | \(-0.545064\pi\) | ||||
−0.141102 | + | 0.989995i | \(0.545064\pi\) | |||||||
\(42\) | 2.28121e16 | + | 3.15330e16i | 1.33559 | + | 1.84617i | ||||
\(43\) | −2.30212e15 | −0.106523 | −0.0532614 | − | 0.998581i | \(-0.516962\pi\) | ||||
−0.0532614 | + | 0.998581i | \(0.516962\pi\) | |||||||
\(44\) | −1.10021e16 | + | 3.33975e16i | −0.404529 | + | 1.22797i | ||||
\(45\) | − | 7.48795e16i | − | 2.19906i | ||||||
\(46\) | −2.06279e16 | − | 2.85139e16i | −0.486270 | − | 0.672168i | ||||
\(47\) | − | 3.45229e16i | − | 0.656340i | −0.944619 | − | 0.328170i | \(-0.893568\pi\) | ||
0.944619 | − | 0.328170i | \(-0.106432\pi\) | |||||||
\(48\) | 9.13223e16 | + | 6.74930e16i | 1.40658 | + | 1.03955i | ||||
\(49\) | −5.56357e16 | −0.697256 | ||||||||
\(50\) | −1.11189e16 | + | 8.04382e15i | −0.113858 | + | 0.0823687i | ||||
\(51\) | 1.65203e16 | 0.138777 | ||||||||
\(52\) | 1.94519e17 | + | 6.40802e16i | 1.34564 | + | 0.443292i | ||||
\(53\) | − | 3.51656e16i | − | 0.201076i | −0.994933 | − | 0.100538i | \(-0.967944\pi\) | ||
0.994933 | − | 0.100538i | \(-0.0320563\pi\) | |||||||
\(54\) | −3.16437e17 | + | 2.28922e17i | −1.50089 | + | 1.08580i | ||||
\(55\) | 3.49736e17i | 1.38074i | ||||||||
\(56\) | −3.76542e17 | + | 1.19807e17i | −1.24146 | + | 0.395006i | ||||
\(57\) | −5.06529e17 | −1.39912 | ||||||||
\(58\) | 6.45338e16 | + | 8.92047e16i | 0.149799 | + | 0.207066i | ||||
\(59\) | 2.54124e17 | 0.497194 | 0.248597 | − | 0.968607i | \(-0.420030\pi\) | ||||
0.248597 | + | 0.968607i | \(0.420030\pi\) | |||||||
\(60\) | 1.07273e18 | + | 3.53390e17i | 1.77411 | + | 0.584443i | ||||
\(61\) | − | 1.01336e18i | − | 1.42057i | −0.703912 | − | 0.710287i | \(-0.748565\pi\) | ||
0.703912 | − | 0.710287i | \(-0.251435\pi\) | |||||||
\(62\) | 1.85989e16 | + | 2.57091e16i | 0.0221600 | + | 0.0306316i | ||||
\(63\) | − | 2.64219e18i | − | 2.68262i | ||||||
\(64\) | −9.40944e17 | + | 6.66222e17i | −0.816139 | + | 0.577855i | ||||
\(65\) | 2.03698e18 | 1.51305 | ||||||||
\(66\) | 2.87341e18 | − | 2.07873e18i | 1.83214 | − | 1.32543i | ||||
\(67\) | −2.98877e18 | −1.63963 | −0.819813 | − | 0.572632i | \(-0.805923\pi\) | ||||
−0.819813 | + | 0.572632i | \(0.805923\pi\) | |||||||
\(68\) | −5.24802e16 | + | 1.59306e17i | −0.0248260 | + | 0.0753606i | ||||
\(69\) | 3.54952e18i | 1.45104i | ||||||||
\(70\) | −3.18424e18 | + | 2.30359e18i | −1.12726 | + | 0.815503i | ||||
\(71\) | 8.39501e17i | 0.257892i | 0.991652 | + | 0.128946i | \(0.0411594\pi\) | ||||
−0.991652 | + | 0.128946i | \(0.958841\pi\) | |||||||
\(72\) | −2.33743e18 | − | 7.34631e18i | −0.624330 | − | 1.96221i | ||||
\(73\) | 3.32042e18 | 0.772617 | 0.386308 | − | 0.922370i | \(-0.373750\pi\) | ||||
0.386308 | + | 0.922370i | \(0.373750\pi\) | |||||||
\(74\) | 2.56253e18 | + | 3.54216e18i | 0.520417 | + | 0.719368i | ||||
\(75\) | 1.38413e18 | 0.245789 | ||||||||
\(76\) | 1.60909e18 | − | 4.88449e18i | 0.250291 | − | 0.759773i | ||||
\(77\) | 1.23407e19i | 1.68436i | ||||||||
\(78\) | −1.21072e19 | − | 1.67357e19i | −1.45244 | − | 2.00770i | ||||
\(79\) | 1.22738e19i | 1.29631i | 0.761510 | + | 0.648153i | \(0.224458\pi\) | ||||
−0.761510 | + | 0.648153i | \(0.775542\pi\) | |||||||
\(80\) | −6.81553e18 | + | 9.22185e18i | −0.634746 | + | 0.858851i | ||||
\(81\) | 1.43570e19 | 1.18090 | ||||||||
\(82\) | −3.14267e18 | + | 2.27352e18i | −0.228644 | + | 0.165409i | ||||
\(83\) | −2.23129e19 | −1.43805 | −0.719027 | − | 0.694982i | \(-0.755412\pi\) | ||||
−0.719027 | + | 0.694982i | \(0.755412\pi\) | |||||||
\(84\) | 3.78524e19 | + | 1.24697e19i | 2.16422 | + | 0.712956i | ||||
\(85\) | 1.66824e18i | 0.0847363i | ||||||||
\(86\) | −1.90997e18 | + | 1.38174e18i | −0.0863061 | + | 0.0624369i | ||||
\(87\) | − | 1.11045e19i | − | 0.447001i | ||||||
\(88\) | 1.09173e19 | + | 3.43120e19i | 0.392003 | + | 1.23203i | ||||
\(89\) | −3.15513e19 | −1.01185 | −0.505926 | − | 0.862577i | \(-0.668849\pi\) | ||||
−0.505926 | + | 0.862577i | \(0.668849\pi\) | |||||||
\(90\) | −4.49430e19 | − | 6.21244e19i | −1.28895 | − | 1.78171i | ||||
\(91\) | 7.18767e19 | 1.84576 | ||||||||
\(92\) | −3.42282e19 | − | 1.12758e19i | −0.787964 | − | 0.259578i | ||||
\(93\) | − | 3.20037e18i | − | 0.0661258i | ||||||
\(94\) | −2.07208e19 | − | 2.86422e19i | −0.384705 | − | 0.531775i | ||||
\(95\) | − | 5.11499e19i | − | 0.854297i | ||||||
\(96\) | 1.16276e20 | + | 1.18413e18i | 1.74895 | + | 0.0178110i | ||||
\(97\) | 8.67034e19 | 1.17576 | 0.587880 | − | 0.808948i | \(-0.299963\pi\) | ||||
0.587880 | + | 0.808948i | \(0.299963\pi\) | |||||||
\(98\) | −4.61586e19 | + | 3.33927e19i | −0.564926 | + | 0.408687i | ||||
\(99\) | −2.40767e20 | −2.66223 | ||||||||
\(100\) | −4.39696e18 | + | 1.33472e19i | −0.0439696 | + | 0.133472i | ||||
\(101\) | 1.28845e20i | 1.16642i | 0.812323 | + | 0.583208i | \(0.198203\pi\) | ||||
−0.812323 | + | 0.583208i | \(0.801797\pi\) | |||||||
\(102\) | 1.37062e19 | − | 9.91554e18i | 0.112438 | − | 0.0813419i | ||||
\(103\) | − | 1.79112e20i | − | 1.33277i | −0.745610 | − | 0.666383i | \(-0.767842\pi\) | ||
0.745610 | − | 0.666383i | \(-0.232158\pi\) | |||||||
\(104\) | 1.99845e20 | − | 6.35863e19i | 1.35008 | − | 0.429566i | ||||
\(105\) | 3.96387e20 | 2.43347 | ||||||||
\(106\) | −2.11065e19 | − | 2.91754e19i | −0.117858 | − | 0.162914i | ||||
\(107\) | −2.99118e20 | −1.52056 | −0.760282 | − | 0.649593i | \(-0.774939\pi\) | ||||
−0.760282 | + | 0.649593i | \(0.774939\pi\) | |||||||
\(108\) | −1.25135e20 | + | 3.79853e20i | −0.579616 | + | 1.75946i | ||||
\(109\) | − | 3.19327e20i | − | 1.34887i | −0.738334 | − | 0.674435i | \(-0.764387\pi\) | ||
0.738334 | − | 0.674435i | \(-0.235613\pi\) | |||||||
\(110\) | 2.09913e20 | + | 2.90161e20i | 0.809304 | + | 1.11870i | ||||
\(111\) | − | 4.40942e20i | − | 1.55293i | ||||||
\(112\) | −2.40492e20 | + | 3.25401e20i | −0.774321 | + | 1.04770i | ||||
\(113\) | −2.35418e20 | −0.693515 | −0.346758 | − | 0.937955i | \(-0.612717\pi\) | ||||
−0.346758 | + | 0.937955i | \(0.612717\pi\) | |||||||
\(114\) | −4.20245e20 | + | 3.04020e20i | −1.13359 | + | 0.820076i | ||||
\(115\) | −3.58435e20 | −0.885996 | ||||||||
\(116\) | 1.07082e20 | + | 3.52759e19i | 0.242737 | + | 0.0799647i | ||||
\(117\) | 1.40231e21i | 2.91733i | ||||||||
\(118\) | 2.10836e20 | − | 1.52526e20i | 0.402833 | − | 0.291424i | ||||
\(119\) | 5.88654e19i | 0.103369i | ||||||||
\(120\) | 1.10211e21 | − | 3.50667e20i | 1.77997 | − | 0.566346i | ||||
\(121\) | 4.51788e20 | 0.671554 | ||||||||
\(122\) | −6.08221e20 | − | 8.40739e20i | −0.832651 | − | 1.15097i | ||||
\(123\) | 3.91212e20 | 0.493584 | ||||||||
\(124\) | 3.08614e19 | + | 1.01666e19i | 0.0359086 | + | 0.0118293i | ||||
\(125\) | − | 8.54840e20i | − | 0.917877i | ||||||
\(126\) | −1.58585e21 | − | 2.19211e21i | −1.57238 | − | 2.17349i | ||||
\(127\) | 5.48014e20i | 0.502058i | 0.967980 | + | 0.251029i | \(0.0807690\pi\) | ||||
−0.967980 | + | 0.251029i | \(0.919231\pi\) | |||||||
\(128\) | −3.80793e20 | + | 1.11749e21i | −0.322544 | + | 0.946554i | ||||
\(129\) | 2.37760e20 | 0.186313 | ||||||||
\(130\) | 1.69000e21 | − | 1.22260e21i | 1.22589 | − | 0.886854i | ||||
\(131\) | 2.37091e21 | 1.59295 | 0.796474 | − | 0.604673i | \(-0.206696\pi\) | ||||
0.796474 | + | 0.604673i | \(0.206696\pi\) | |||||||
\(132\) | 1.13629e21 | − | 3.44926e21i | 0.707537 | − | 2.14777i | ||||
\(133\) | − | 1.80487e21i | − | 1.04215i | ||||||
\(134\) | −2.47966e21 | + | 1.79387e21i | −1.32844 | + | 0.961044i | ||||
\(135\) | 3.97779e21i | 1.97835i | ||||||||
\(136\) | 5.20757e19 | + | 1.63669e20i | 0.0240573 | + | 0.0756095i | ||||
\(137\) | −1.87304e21 | −0.804158 | −0.402079 | − | 0.915605i | \(-0.631712\pi\) | ||||
−0.402079 | + | 0.915605i | \(0.631712\pi\) | |||||||
\(138\) | 2.13043e21 | + | 2.94488e21i | 0.850505 | + | 1.17565i | ||||
\(139\) | −4.17320e21 | −1.54996 | −0.774982 | − | 0.631983i | \(-0.782241\pi\) | ||||
−0.774982 | + | 0.631983i | \(0.782241\pi\) | |||||||
\(140\) | −1.25921e21 | + | 3.82239e21i | −0.435328 | + | 1.32146i | ||||
\(141\) | 3.56549e21i | 1.14796i | ||||||||
\(142\) | 5.03872e20 | + | 6.96498e20i | 0.151160 | + | 0.208947i | ||||
\(143\) | − | 6.54970e21i | − | 1.83173i | ||||||
\(144\) | −6.34855e21 | − | 4.69199e21i | −1.65596 | − | 1.22386i | ||||
\(145\) | 1.12135e21 | 0.272937 | ||||||||
\(146\) | 2.75481e21 | − | 1.99293e21i | 0.625984 | − | 0.452859i | ||||
\(147\) | 5.74599e21 | 1.21953 | ||||||||
\(148\) | 4.25204e21 | + | 1.40075e21i | 0.843296 | + | 0.277806i | ||||
\(149\) | 4.63926e21i | 0.860174i | 0.902787 | + | 0.430087i | \(0.141517\pi\) | ||||
−0.902787 | + | 0.430087i | \(0.858483\pi\) | |||||||
\(150\) | 1.14835e21 | − | 8.30757e20i | 0.199141 | − | 0.144066i | ||||
\(151\) | 6.55978e21i | 1.06444i | 0.846607 | + | 0.532218i | \(0.178641\pi\) | ||||
−0.846607 | + | 0.532218i | \(0.821359\pi\) | |||||||
\(152\) | −1.59669e21 | − | 5.01824e21i | −0.242541 | − | 0.762282i | ||||
\(153\) | −1.14846e21 | −0.163381 | ||||||||
\(154\) | 7.40696e21 | + | 1.02386e22i | 0.987262 | + | 1.36469i | ||||
\(155\) | 3.23178e20 | 0.0403761 | ||||||||
\(156\) | −2.00897e22 | − | 6.61813e21i | −2.35357 | − | 0.775335i | ||||
\(157\) | − | 1.23081e22i | − | 1.35268i | −0.736589 | − | 0.676340i | \(-0.763565\pi\) | ||
0.736589 | − | 0.676340i | \(-0.236435\pi\) | |||||||
\(158\) | 7.36677e21 | + | 1.01830e22i | 0.759812 | + | 1.05028i | ||||
\(159\) | 3.63187e21i | 0.351689i | ||||||||
\(160\) | −1.19575e20 | + | 1.17417e22i | −0.0108753 | + | 1.06790i | ||||
\(161\) | −1.26477e22 | −1.08082 | ||||||||
\(162\) | 1.19114e22 | − | 8.61715e21i | 0.956783 | − | 0.692171i | ||||
\(163\) | −1.08316e21 | −0.0818120 | −0.0409060 | − | 0.999163i | \(-0.513024\pi\) | ||||
−0.0409060 | + | 0.999163i | \(0.513024\pi\) | |||||||
\(164\) | −1.24277e21 | + | 3.77249e21i | −0.0882981 | + | 0.268034i | ||||
\(165\) | − | 3.61204e22i | − | 2.41497i | ||||||
\(166\) | −1.85121e22 | + | 1.33923e22i | −1.16513 | + | 0.842896i | ||||
\(167\) | − | 1.57673e22i | − | 0.934531i | −0.884117 | − | 0.467266i | \(-0.845239\pi\) | ||
0.884117 | − | 0.467266i | \(-0.154761\pi\) | |||||||
\(168\) | 3.88889e22 | − | 1.23736e22i | 2.17136 | − | 0.690880i | ||||
\(169\) | −1.91427e22 | −1.00725 | ||||||||
\(170\) | 1.00128e21 | + | 1.38407e21i | 0.0496670 | + | 0.0686544i | ||||
\(171\) | 3.52129e22 | 1.64718 | ||||||||
\(172\) | −7.55295e20 | + | 2.29274e21i | −0.0333298 | + | 0.101174i | ||||
\(173\) | − | 1.33989e22i | − | 0.557968i | −0.960296 | − | 0.278984i | \(-0.910002\pi\) | ||
0.960296 | − | 0.278984i | \(-0.0899976\pi\) | |||||||
\(174\) | −6.66499e21 | − | 9.21297e21i | −0.262003 | − | 0.362166i | ||||
\(175\) | 4.93194e21i | 0.183078i | ||||||||
\(176\) | 2.96519e22 | + | 2.19146e22i | 1.03974 | + | 0.768435i | ||||
\(177\) | −2.62457e22 | −0.869612 | ||||||||
\(178\) | −2.61768e22 | + | 1.89372e22i | −0.819816 | + | 0.593084i | ||||
\(179\) | 1.76290e22 | 0.522032 | 0.261016 | − | 0.965334i | \(-0.415942\pi\) | ||||
0.261016 | + | 0.965334i | \(0.415942\pi\) | |||||||
\(180\) | −7.45745e22 | − | 2.45670e22i | −2.08865 | − | 0.688062i | ||||
\(181\) | 3.12653e22i | 0.828469i | 0.910170 | + | 0.414235i | \(0.135951\pi\) | ||||
−0.910170 | + | 0.414235i | \(0.864049\pi\) | |||||||
\(182\) | 5.96331e22 | − | 4.31407e22i | 1.49545 | − | 1.08186i | ||||
\(183\) | 1.04658e23i | 2.48464i | ||||||||
\(184\) | −3.51655e22 | + | 1.11889e22i | −0.790566 | + | 0.251541i | ||||
\(185\) | 4.45269e22 | 0.948212 | ||||||||
\(186\) | −1.92087e21 | − | 2.65521e21i | −0.0387587 | − | 0.0535759i | ||||
\(187\) | 5.36405e21 | 0.102583 | ||||||||
\(188\) | −3.43823e22 | − | 1.13265e22i | −0.623385 | − | 0.205361i | ||||
\(189\) | 1.40360e23i | 2.41337i | ||||||||
\(190\) | −3.07004e22 | − | 4.24369e22i | −0.500735 | − | 0.692162i | ||||
\(191\) | − | 8.00644e22i | − | 1.23910i | −0.784958 | − | 0.619549i | \(-0.787315\pi\) | ||
0.784958 | − | 0.619549i | \(-0.212685\pi\) | |||||||
\(192\) | 9.71798e22 | − | 6.88067e22i | 1.42746 | − | 1.01069i | ||||
\(193\) | 4.76538e21 | 0.0664544 | 0.0332272 | − | 0.999448i | \(-0.489421\pi\) | ||||
0.0332272 | + | 0.999448i | \(0.489421\pi\) | |||||||
\(194\) | 7.19341e22 | − | 5.20397e22i | 0.952615 | − | 0.689155i | ||||
\(195\) | −2.10377e23 | −2.64639 | ||||||||
\(196\) | −1.82534e22 | + | 5.54091e22i | −0.218163 | + | 0.662247i | ||||
\(197\) | − | 3.59368e22i | − | 0.408204i | −0.978950 | − | 0.204102i | \(-0.934573\pi\) | ||
0.978950 | − | 0.204102i | \(-0.0654274\pi\) | |||||||
\(198\) | −1.99754e23 | + | 1.44509e23i | −2.15697 | + | 1.56043i | ||||
\(199\) | − | 1.66755e22i | − | 0.171218i | −0.996329 | − | 0.0856088i | \(-0.972716\pi\) | ||
0.996329 | − | 0.0856088i | \(-0.0272835\pi\) | |||||||
\(200\) | 4.36308e21 | + | 1.37127e22i | 0.0426082 | + | 0.133913i | ||||
\(201\) | 3.08677e23 | 2.86777 | ||||||||
\(202\) | 7.73331e22 | + | 1.06897e23i | 0.683678 | + | 0.945044i | ||||
\(203\) | 3.95679e22 | 0.332953 | ||||||||
\(204\) | 5.42010e21 | − | 1.64530e22i | 0.0434216 | − | 0.131809i | ||||
\(205\) | 3.95051e22i | 0.301380i | ||||||||
\(206\) | −1.07504e23 | − | 1.48602e23i | −0.781182 | − | 1.07982i | ||||
\(207\) | − | 2.46756e23i | − | 1.70830i | ||||||
\(208\) | 1.27638e23 | − | 1.72703e23i | 0.842069 | − | 1.13937i | ||||
\(209\) | −1.64467e23 | −1.03423 | ||||||||
\(210\) | 3.28865e23 | − | 2.37913e23i | 1.97163 | − | 1.42635i | ||||
\(211\) | 5.82077e22 | 0.332779 | 0.166390 | − | 0.986060i | \(-0.446789\pi\) | ||||
0.166390 | + | 0.986060i | \(0.446789\pi\) | |||||||
\(212\) | −3.50224e22 | − | 1.15374e22i | −0.190980 | − | 0.0629142i | ||||
\(213\) | − | 8.67028e22i | − | 0.451063i | ||||||
\(214\) | −2.48165e23 | + | 1.79532e23i | −1.23198 | + | 0.891258i | ||||
\(215\) | 2.40093e22i | 0.113762i | ||||||||
\(216\) | 1.24170e23 | + | 3.90255e23i | 0.561669 | + | 1.76527i | ||||
\(217\) | 1.14036e22 | 0.0492544 | ||||||||
\(218\) | −1.91661e23 | − | 2.64932e23i | −0.790622 | − | 1.09287i | ||||
\(219\) | −3.42929e23 | −1.35134 | ||||||||
\(220\) | 3.48311e23 | + | 1.14744e23i | 1.31142 | + | 0.432019i | ||||
\(221\) | − | 3.12421e22i | − | 0.112413i | ||||||
\(222\) | −2.64655e23 | − | 3.65831e23i | −0.910229 | − | 1.25820i | ||||
\(223\) | 5.04418e23i | 1.65860i | 0.558803 | + | 0.829301i | \(0.311261\pi\) | ||||
−0.558803 | + | 0.829301i | \(0.688739\pi\) | |||||||
\(224\) | −4.21933e21 | + | 4.14316e23i | −0.0132667 | + | 1.30272i | ||||
\(225\) | −9.62218e22 | −0.289367 | ||||||||
\(226\) | −1.95317e23 | + | 1.41299e23i | −0.561895 | + | 0.406495i | ||||
\(227\) | 4.05442e23 | 1.11602 | 0.558008 | − | 0.829835i | \(-0.311566\pi\) | ||||
0.558008 | + | 0.829835i | \(0.311566\pi\) | |||||||
\(228\) | −1.66186e23 | + | 5.04465e23i | −0.437769 | + | 1.32887i | ||||
\(229\) | 4.75091e23i | 1.19790i | 0.800785 | + | 0.598952i | \(0.204416\pi\) | ||||
−0.800785 | + | 0.598952i | \(0.795584\pi\) | |||||||
\(230\) | −2.97378e23 | + | 2.15134e23i | −0.717845 | + | 0.519315i | ||||
\(231\) | − | 1.27454e24i | − | 2.94600i | ||||||
\(232\) | 1.10014e23 | − | 3.50040e22i | 0.243539 | − | 0.0774887i | ||||
\(233\) | 6.24482e22 | 0.132422 | 0.0662110 | − | 0.997806i | \(-0.478909\pi\) | ||||
0.0662110 | + | 0.997806i | \(0.478909\pi\) | |||||||
\(234\) | 8.41672e23 | + | 1.16344e24i | 1.70995 | + | 2.36366i | ||||
\(235\) | −3.60048e23 | −0.700942 | ||||||||
\(236\) | 8.33750e22 | − | 2.53089e23i | 0.155566 | − | 0.472230i | ||||
\(237\) | − | 1.26762e24i | − | 2.26729i | ||||||
\(238\) | 3.53312e22 | + | 4.88381e22i | 0.0605883 | + | 0.0837508i | ||||
\(239\) | 4.38763e23i | 0.721525i | 0.932658 | + | 0.360763i | \(0.117484\pi\) | ||||
−0.932658 | + | 0.360763i | \(0.882516\pi\) | |||||||
\(240\) | 7.03901e23 | − | 9.52423e23i | 1.11020 | − | 1.50216i | ||||
\(241\) | −6.38433e23 | −0.965928 | −0.482964 | − | 0.875640i | \(-0.660440\pi\) | ||||
−0.482964 | + | 0.875640i | \(0.660440\pi\) | |||||||
\(242\) | 3.74829e23 | − | 2.71165e23i | 0.544102 | − | 0.393622i | ||||
\(243\) | −1.52896e23 | −0.212978 | ||||||||
\(244\) | −1.00923e24 | − | 3.32470e23i | −1.34925 | − | 0.444481i | ||||
\(245\) | 5.80238e23i | 0.744639i | ||||||||
\(246\) | 3.24572e23 | − | 2.34807e23i | 0.399908 | − | 0.289308i | ||||
\(247\) | 9.57913e23i | 1.13333i | ||||||||
\(248\) | 3.17065e22 | − | 1.00883e22i | 0.0360272 | − | 0.0114631i | ||||
\(249\) | 2.30445e24 | 2.51521 | ||||||||
\(250\) | −5.13078e23 | − | 7.09224e23i | −0.538001 | − | 0.743676i | ||||
\(251\) | −4.03875e23 | −0.406921 | −0.203460 | − | 0.979083i | \(-0.565219\pi\) | ||||
−0.203460 | + | 0.979083i | \(0.565219\pi\) | |||||||
\(252\) | −2.63143e24 | − | 8.66869e23i | −2.54792 | − | 0.839360i | ||||
\(253\) | 1.15251e24i | 1.07260i | ||||||||
\(254\) | 3.28920e23 | + | 4.54664e23i | 0.294275 | + | 0.406774i | ||||
\(255\) | − | 1.72294e23i | − | 0.148207i | ||||||
\(256\) | 3.54796e23 | + | 1.15569e24i | 0.293481 | + | 0.955965i | ||||
\(257\) | −1.49185e24 | −1.18685 | −0.593424 | − | 0.804890i | \(-0.702224\pi\) | ||||
−0.593424 | + | 0.804890i | \(0.702224\pi\) | |||||||
\(258\) | 1.97260e23 | − | 1.42705e23i | 0.150953 | − | 0.109205i | ||||
\(259\) | 1.57117e24 | 1.15671 | ||||||||
\(260\) | 6.68308e23 | − | 2.02869e24i | 0.473416 | − | 1.43708i | ||||
\(261\) | 7.71967e23i | 0.526252i | ||||||||
\(262\) | 1.96704e24 | − | 1.42303e24i | 1.29063 | − | 0.933684i | ||||
\(263\) | 3.50322e23i | 0.221263i | 0.993861 | + | 0.110632i | \(0.0352874\pi\) | ||||
−0.993861 | + | 0.110632i | \(0.964713\pi\) | |||||||
\(264\) | −1.12753e24 | − | 3.54371e24i | −0.685629 | − | 2.15486i | ||||
\(265\) | −3.66751e23 | −0.214740 | ||||||||
\(266\) | −1.08329e24 | − | 1.49742e24i | −0.610841 | − | 0.844362i | ||||
\(267\) | 3.25859e24 | 1.76977 | ||||||||
\(268\) | −9.80578e23 | + | 2.97660e24i | −0.513020 | + | 1.55730i | ||||
\(269\) | − | 2.56975e24i | − | 1.29529i | −0.761941 | − | 0.647646i | \(-0.775754\pi\) | ||
0.761941 | − | 0.647646i | \(-0.224246\pi\) | |||||||
\(270\) | 2.38748e24 | + | 3.30020e24i | 1.15959 | + | 1.60289i | ||||
\(271\) | 3.31630e24i | 1.55225i | 0.630582 | + | 0.776123i | \(0.282816\pi\) | ||||
−0.630582 | + | 0.776123i | \(0.717184\pi\) | |||||||
\(272\) | 1.41439e23 | + | 1.04533e23i | 0.0638089 | + | 0.0471589i | ||||
\(273\) | −7.42335e24 | −3.22830 | ||||||||
\(274\) | −1.55398e24 | + | 1.12421e24i | −0.651539 | + | 0.471346i | ||||
\(275\) | 4.49418e23 | 0.181687 | ||||||||
\(276\) | 3.53506e24 | + | 1.16455e24i | 1.37818 | + | 0.454012i | ||||
\(277\) | − | 4.21196e24i | − | 1.58375i | −0.610683 | − | 0.791876i | \(-0.709105\pi\) | ||
0.610683 | − | 0.791876i | \(-0.290895\pi\) | |||||||
\(278\) | −3.46233e24 | + | 2.50477e24i | −1.25580 | + | 0.908490i | ||||
\(279\) | 2.22484e23i | 0.0778496i | ||||||||
\(280\) | 1.24950e24 | + | 3.92705e24i | 0.421848 | + | 1.32583i | ||||
\(281\) | 4.42895e24 | 1.44290 | 0.721452 | − | 0.692465i | \(-0.243475\pi\) | ||||
0.721452 | + | 0.692465i | \(0.243475\pi\) | |||||||
\(282\) | 2.14002e24 | + | 2.95814e24i | 0.672864 | + | 0.930095i | ||||
\(283\) | 1.44352e24 | 0.438086 | 0.219043 | − | 0.975715i | \(-0.429706\pi\) | ||||
0.219043 | + | 0.975715i | \(0.429706\pi\) | |||||||
\(284\) | 8.36082e23 | + | 2.75430e23i | 0.244943 | + | 0.0806914i | ||||
\(285\) | 5.28271e24i | 1.49420i | ||||||||
\(286\) | −3.93115e24 | − | 5.43401e24i | −1.07364 | − | 1.48409i | ||||
\(287\) | 1.39397e24i | 0.367651i | ||||||||
\(288\) | −8.08327e24 | − | 8.23188e22i | −2.05903 | − | 0.0209688i | ||||
\(289\) | −4.03864e24 | −0.993704 | ||||||||
\(290\) | 9.30338e23 | − | 6.73039e23i | 0.221137 | − | 0.159978i | ||||
\(291\) | −8.95463e24 | −2.05645 | ||||||||
\(292\) | 1.08939e24 | − | 3.30689e24i | 0.241743 | − | 0.733824i | ||||
\(293\) | − | 8.90093e24i | − | 1.90879i | −0.298541 | − | 0.954397i | \(-0.596500\pi\) | ||
0.298541 | − | 0.954397i | \(-0.403500\pi\) | |||||||
\(294\) | 4.76721e24 | − | 3.44877e24i | 0.988077 | − | 0.714810i | ||||
\(295\) | − | 2.65033e24i | − | 0.530981i | ||||||
\(296\) | 4.36847e24 | − | 1.38995e24i | 0.846081 | − | 0.269204i | ||||
\(297\) | 1.27902e25 | 2.39503 | ||||||||
\(298\) | 2.78450e24 | + | 3.84900e24i | 0.504179 | + | 0.696924i | ||||
\(299\) | 6.71261e24 | 1.17538 | ||||||||
\(300\) | 4.54114e23 | − | 1.37849e24i | 0.0769046 | − | 0.233448i | ||||
\(301\) | 8.47191e23i | 0.138777i | ||||||||
\(302\) | 3.93720e24 | + | 5.44237e24i | 0.623905 | + | 0.862420i | ||||
\(303\) | − | 1.33070e25i | − | 2.04011i | ||||||
\(304\) | −4.33667e24 | − | 3.20508e24i | −0.643311 | − | 0.475448i | ||||
\(305\) | −1.05686e25 | −1.51711 | ||||||||
\(306\) | −9.52828e23 | + | 6.89310e23i | −0.132373 | + | 0.0957635i | ||||
\(307\) | 8.30730e23 | 0.111706 | 0.0558529 | − | 0.998439i | \(-0.482212\pi\) | ||||
0.0558529 | + | 0.998439i | \(0.482212\pi\) | |||||||
\(308\) | 1.22905e25 | + | 4.04884e24i | 1.59978 | + | 0.527016i | ||||
\(309\) | 1.84986e25i | 2.33106i | ||||||||
\(310\) | 2.68127e23 | − | 1.93972e23i | 0.0327132 | − | 0.0236659i | ||||
\(311\) | − | 1.01133e25i | − | 1.19478i | −0.801951 | − | 0.597390i | \(-0.796204\pi\) | ||
0.801951 | − | 0.597390i | \(-0.203796\pi\) | |||||||
\(312\) | −2.06398e25 | + | 6.56713e24i | −2.36135 | + | 0.751328i | ||||
\(313\) | 6.25698e24 | 0.693300 | 0.346650 | − | 0.937995i | \(-0.387319\pi\) | ||||
0.346650 | + | 0.937995i | \(0.387319\pi\) | |||||||
\(314\) | −7.38738e24 | − | 1.02115e25i | −0.792855 | − | 1.09596i | ||||
\(315\) | −2.75561e25 | −2.86491 | ||||||||
\(316\) | 1.22238e25 | + | 4.02687e24i | 1.23122 | + | 0.405599i | ||||
\(317\) | − | 6.36417e24i | − | 0.621083i | −0.950560 | − | 0.310541i | \(-0.899490\pi\) | ||
0.950560 | − | 0.310541i | \(-0.100510\pi\) | |||||||
\(318\) | 2.17986e24 | + | 3.01321e24i | 0.206138 | + | 0.284943i | ||||
\(319\) | − | 3.60559e24i | − | 0.330422i | ||||||
\(320\) | 6.94819e24 | + | 9.81334e24i | 0.617124 | + | 0.871600i | ||||
\(321\) | 3.08926e25 | 2.65953 | ||||||||
\(322\) | −1.04933e25 | + | 7.59119e24i | −0.875692 | + | 0.633507i | ||||
\(323\) | −7.84509e23 | −0.0634706 | ||||||||
\(324\) | 4.71036e24 | − | 1.42986e25i | 0.369491 | − | 1.12161i | ||||
\(325\) | − | 2.61757e24i | − | 0.199097i | ||||||
\(326\) | −8.98652e23 | + | 6.50117e23i | −0.0662851 | + | 0.0479530i | ||||
\(327\) | 3.29797e25i | 2.35923i | ||||||||
\(328\) | 1.23319e24 | + | 3.87579e24i | 0.0855640 | + | 0.268919i | ||||
\(329\) | −1.27046e25 | −0.855072 | ||||||||
\(330\) | −2.16796e25 | − | 2.99675e25i | −1.41550 | − | 1.95664i | ||||
\(331\) | 1.21569e25 | 0.770093 | 0.385046 | − | 0.922897i | \(-0.374185\pi\) | ||||
0.385046 | + | 0.922897i | \(0.374185\pi\) | |||||||
\(332\) | −7.32058e24 | + | 2.22220e25i | −0.449951 | + | 1.36585i | ||||
\(333\) | 3.06535e25i | 1.82826i | ||||||||
\(334\) | −9.46362e24 | − | 1.30815e25i | −0.547763 | − | 0.757169i | ||||
\(335\) | 3.11706e25i | 1.75105i | ||||||||
\(336\) | 2.48378e25 | − | 3.36071e25i | 1.35432 | − | 1.83247i | ||||
\(337\) | −3.30993e25 | −1.75194 | −0.875970 | − | 0.482366i | \(-0.839778\pi\) | ||||
−0.875970 | + | 0.482366i | \(0.839778\pi\) | |||||||
\(338\) | −1.58819e25 | + | 1.14895e25i | −0.816086 | + | 0.590385i | ||||
\(339\) | 2.43138e25 | 1.21299 | ||||||||
\(340\) | 1.66145e24 | + | 5.47329e23i | 0.0804817 | + | 0.0265130i | ||||
\(341\) | − | 1.03914e24i | − | 0.0488800i | ||||||
\(342\) | 2.92147e25 | − | 2.11349e25i | 1.33457 | − | 0.965472i | ||||
\(343\) | − | 8.88976e24i | − | 0.394411i | ||||||
\(344\) | 7.49474e23 | + | 2.35552e24i | 0.0322977 | + | 0.101508i | ||||
\(345\) | 3.70188e25 | 1.54964 | ||||||||
\(346\) | −8.04209e24 | − | 1.11165e25i | −0.327045 | − | 0.452073i | ||||
\(347\) | −1.29207e25 | −0.510493 | −0.255247 | − | 0.966876i | \(-0.582157\pi\) | ||||
−0.255247 | + | 0.966876i | \(0.582157\pi\) | |||||||
\(348\) | −1.10593e25 | − | 3.64326e24i | −0.424557 | − | 0.139861i | ||||
\(349\) | − | 1.52161e25i | − | 0.567608i | −0.958882 | − | 0.283804i | \(-0.908403\pi\) | ||
0.958882 | − | 0.283804i | \(-0.0915965\pi\) | |||||||
\(350\) | 2.96017e24 | + | 4.09182e24i | 0.107309 | + | 0.148332i | ||||
\(351\) | − | 7.44943e25i | − | 2.62453i | ||||||
\(352\) | 3.77541e25 | + | 3.84482e23i | 1.29282 | + | 0.0131659i | ||||
\(353\) | 1.15184e24 | 0.0383394 | 0.0191697 | − | 0.999816i | \(-0.493898\pi\) | ||||
0.0191697 | + | 0.999816i | \(0.493898\pi\) | |||||||
\(354\) | −2.17749e25 | + | 1.57528e25i | −0.704571 | + | 0.509711i | ||||
\(355\) | 8.75537e24 | 0.275417 | ||||||||
\(356\) | −1.03516e25 | + | 3.14228e25i | −0.316597 | + | 0.961047i | ||||
\(357\) | − | 6.07956e24i | − | 0.180796i | ||||||
\(358\) | 1.46260e25 | − | 1.05810e25i | 0.422957 | − | 0.305982i | ||||
\(359\) | − | 1.62522e25i | − | 0.457053i | −0.973538 | − | 0.228527i | \(-0.926609\pi\) | ||
0.973538 | − | 0.228527i | \(-0.0733908\pi\) | |||||||
\(360\) | −7.66165e25 | + | 2.43777e25i | −2.09555 | + | 0.666757i | ||||
\(361\) | −1.35362e25 | −0.360100 | ||||||||
\(362\) | 1.87655e25 | + | 2.59395e25i | 0.485596 | + | 0.671236i | ||||
\(363\) | −4.66602e25 | −1.17457 | ||||||||
\(364\) | 2.35818e25 | − | 7.15840e25i | 0.577516 | − | 1.75308i | ||||
\(365\) | − | 3.46295e25i | − | 0.825120i | ||||||
\(366\) | 6.28164e25 | + | 8.68307e25i | 1.45634 | + | 2.01309i | ||||
\(367\) | 1.86174e25i | 0.420009i | 0.977700 | + | 0.210004i | \(0.0673478\pi\) | ||||
−0.977700 | + | 0.210004i | \(0.932652\pi\) | |||||||
\(368\) | −2.24597e25 | + | 3.03894e25i | −0.493090 | + | 0.667181i | ||||
\(369\) | −2.71963e25 | −0.581094 | ||||||||
\(370\) | 3.69421e25 | − | 2.67252e25i | 0.768253 | − | 0.555782i | ||||
\(371\) | −1.29411e25 | −0.261959 | ||||||||
\(372\) | −3.18733e24 | − | 1.05000e24i | −0.0628056 | − | 0.0206900i | ||||
\(373\) | − | 8.50867e24i | − | 0.163220i | −0.996664 | − | 0.0816100i | \(-0.973994\pi\) | ||
0.996664 | − | 0.0816100i | \(-0.0260062\pi\) | |||||||
\(374\) | 4.45033e24 | − | 3.21952e24i | 0.0831143 | − | 0.0601278i | ||||
\(375\) | 8.82870e25i | 1.60540i | ||||||||
\(376\) | −3.53238e25 | + | 1.12392e25i | −0.625444 | + | 0.199003i | ||||
\(377\) | −2.10002e25 | −0.362084 | ||||||||
\(378\) | 8.42445e25 | + | 1.16451e26i | 1.41457 | + | 1.95535i | ||||
\(379\) | 7.81947e25 | 1.27875 | 0.639375 | − | 0.768895i | \(-0.279193\pi\) | ||||
0.639375 | + | 0.768895i | \(0.279193\pi\) | |||||||
\(380\) | −5.09416e25 | − | 1.67816e25i | −0.811403 | − | 0.267300i | ||||
\(381\) | − | 5.65983e25i | − | 0.878119i | ||||||
\(382\) | −4.80549e25 | − | 6.64260e25i | −0.726281 | − | 1.00393i | ||||
\(383\) | − | 5.58884e25i | − | 0.822875i | −0.911438 | − | 0.411438i | \(-0.865027\pi\) | ||
0.911438 | − | 0.411438i | \(-0.134973\pi\) | |||||||
\(384\) | 3.93279e25 | − | 1.15414e26i | 0.564142 | − | 1.65556i | ||||
\(385\) | 1.28705e26 | 1.79882 | ||||||||
\(386\) | 3.95363e24 | − | 2.86020e24i | 0.0538422 | − | 0.0389514i | ||||
\(387\) | −1.65286e25 | −0.219345 | ||||||||
\(388\) | 2.84463e25 | − | 8.63502e25i | 0.367882 | − | 1.11672i | ||||
\(389\) | 1.08837e26i | 1.37176i | 0.727714 | + | 0.685881i | \(0.240583\pi\) | ||||
−0.727714 | + | 0.685881i | \(0.759417\pi\) | |||||||
\(390\) | −1.74541e26 | + | 1.26269e26i | −2.14413 | + | 1.55114i | ||||
\(391\) | 5.49747e24i | 0.0658257i | ||||||||
\(392\) | 1.81127e25 | + | 5.69263e25i | 0.211408 | + | 0.664434i | ||||
\(393\) | −2.44865e26 | −2.78613 | ||||||||
\(394\) | −2.15694e25 | − | 2.98153e25i | −0.239263 | − | 0.330732i | ||||
\(395\) | 1.28006e26 | 1.38440 | ||||||||
\(396\) | −7.89926e25 | + | 2.39786e26i | −0.832980 | + | 2.52856i | ||||
\(397\) | − | 6.59942e25i | − | 0.678579i | −0.940682 | − | 0.339290i | \(-0.889813\pi\) | ||
0.940682 | − | 0.339290i | \(-0.110187\pi\) | |||||||
\(398\) | −1.00087e25 | − | 1.38350e25i | −0.100357 | − | 0.138723i | ||||
\(399\) | 1.86405e26i | 1.82276i | ||||||||
\(400\) | 1.18503e25 | + | 8.75811e24i | 0.113013 | + | 0.0835239i | ||||
\(401\) | −1.61721e26 | −1.50426 | −0.752130 | − | 0.659015i | \(-0.770973\pi\) | ||||
−0.752130 | + | 0.659015i | \(0.770973\pi\) | |||||||
\(402\) | 2.56096e26 | − | 1.85269e26i | 2.32350 | − | 1.68090i | ||||
\(403\) | −6.05233e24 | −0.0535639 | ||||||||
\(404\) | 1.28320e26 | + | 4.22723e25i | 1.10785 | + | 0.364958i | ||||
\(405\) | − | 1.49733e26i | − | 1.26115i | ||||||
\(406\) | 3.28278e25 | − | 2.37488e25i | 0.269762 | − | 0.195156i | ||||
\(407\) | − | 1.43172e26i | − | 1.14792i | ||||||
\(408\) | −5.37833e24 | − | 1.69035e25i | −0.0420771 | − | 0.132244i | ||||
\(409\) | −4.61427e25 | −0.352266 | −0.176133 | − | 0.984366i | \(-0.556359\pi\) | ||||
−0.176133 | + | 0.984366i | \(0.556359\pi\) | |||||||
\(410\) | 2.37111e25 | + | 3.27757e25i | 0.176650 | + | 0.244182i | ||||
\(411\) | 1.93446e26 | 1.40650 | ||||||||
\(412\) | −1.78383e26 | − | 5.87645e25i | −1.26585 | − | 0.417007i | ||||
\(413\) | − | 9.35191e25i | − | 0.647739i | ||||||
\(414\) | −1.48104e26 | − | 2.04723e26i | −1.00130 | − | 1.38408i | ||||
\(415\) | 2.32707e26i | 1.53578i | ||||||||
\(416\) | 2.23936e24 | − | 2.19893e26i | 0.0144275 | − | 1.41670i | ||||
\(417\) | 4.31004e26 | 2.71095 | ||||||||
\(418\) | −1.36451e26 | + | 9.87138e25i | −0.837944 | + | 0.606199i | ||||
\(419\) | −5.29625e24 | −0.0317562 | −0.0158781 | − | 0.999874i | \(-0.505054\pi\) | ||||
−0.0158781 | + | 0.999874i | \(0.505054\pi\) | |||||||
\(420\) | 1.30049e26 | − | 3.94772e26i | 0.761405 | − | 2.31129i | ||||
\(421\) | 1.49367e26i | 0.853954i | 0.904262 | + | 0.426977i | \(0.140422\pi\) | ||||
−0.904262 | + | 0.426977i | \(0.859578\pi\) | |||||||
\(422\) | 4.82925e25 | − | 3.49365e25i | 0.269622 | − | 0.195054i | ||||
\(423\) | − | 2.47866e26i | − | 1.35149i | ||||||
\(424\) | −3.59813e25 | + | 1.14485e25i | −0.191610 | + | 0.0609661i | ||||
\(425\) | 2.14373e24 | 0.0111501 | ||||||||
\(426\) | −5.20393e25 | − | 7.19336e25i | −0.264384 | − | 0.365457i | ||||
\(427\) | −3.72921e26 | −1.85071 | ||||||||
\(428\) | −9.81368e25 | + | 2.97900e26i | −0.475767 | + | 1.44422i | ||||
\(429\) | 6.76446e26i | 3.20376i | ||||||||
\(430\) | 1.44105e25 | + | 1.99195e25i | 0.0666798 | + | 0.0921711i | ||||
\(431\) | 5.76714e25i | 0.260728i | 0.991466 | + | 0.130364i | \(0.0416146\pi\) | ||||
−0.991466 | + | 0.130364i | \(0.958385\pi\) | |||||||
\(432\) | 3.37251e26 | + | 2.49250e26i | 1.48976 | + | 1.10103i | ||||
\(433\) | 3.62350e26 | 1.56405 | 0.782023 | − | 0.623250i | \(-0.214188\pi\) | ||||
0.782023 | + | 0.623250i | \(0.214188\pi\) | |||||||
\(434\) | 9.46109e24 | − | 6.84449e24i | 0.0399065 | − | 0.0288698i | ||||
\(435\) | −1.15812e26 | −0.477377 | ||||||||
\(436\) | −3.18026e26 | − | 1.04767e26i | −1.28114 | − | 0.422046i | ||||
\(437\) | − | 1.68558e26i | − | 0.663644i | ||||||
\(438\) | −2.84514e26 | + | 2.05827e26i | −1.09487 | + | 0.792067i | ||||
\(439\) | 2.02029e26i | 0.759921i | 0.925003 | + | 0.379960i | \(0.124062\pi\) | ||||
−0.925003 | + | 0.379960i | \(0.875938\pi\) | |||||||
\(440\) | 3.57849e26 | − | 1.13860e26i | 1.31575 | − | 0.418642i | ||||
\(441\) | −3.99451e26 | −1.43575 | ||||||||
\(442\) | −1.87516e25 | − | 2.59202e25i | −0.0658894 | − | 0.0910786i | ||||
\(443\) | −5.17324e26 | −1.77716 | −0.888578 | − | 0.458725i | \(-0.848306\pi\) | ||||
−0.888578 | + | 0.458725i | \(0.848306\pi\) | |||||||
\(444\) | −4.39146e26 | − | 1.44668e26i | −1.47496 | − | 0.485894i | ||||
\(445\) | 3.29056e26i | 1.08061i | ||||||||
\(446\) | 3.02754e26 | + | 4.18494e26i | 0.972167 | + | 1.34382i | ||||
\(447\) | − | 4.79138e26i | − | 1.50448i | ||||||
\(448\) | 2.45173e26 | + | 3.46273e26i | 0.752823 | + | 1.06326i | ||||
\(449\) | 5.37552e26 | 1.61420 | 0.807099 | − | 0.590416i | \(-0.201036\pi\) | ||||
0.807099 | + | 0.590416i | \(0.201036\pi\) | |||||||
\(450\) | −7.98312e25 | + | 5.77527e25i | −0.234448 | + | 0.169608i | ||||
\(451\) | 1.27024e26 | 0.364856 | ||||||||
\(452\) | −7.72378e25 | + | 2.34460e26i | −0.216993 | + | 0.658694i | ||||
\(453\) | − | 6.77487e26i | − | 1.86174i | ||||||
\(454\) | 3.36378e26 | − | 2.43348e26i | 0.904210 | − | 0.654138i | ||||
\(455\) | − | 7.49620e26i | − | 1.97118i | ||||||
\(456\) | 1.64905e26 | + | 5.18279e26i | 0.424214 | + | 1.33326i | ||||
\(457\) | −2.00836e26 | −0.505452 | −0.252726 | − | 0.967538i | \(-0.581327\pi\) | ||||
−0.252726 | + | 0.967538i | \(0.581327\pi\) | |||||||
\(458\) | 2.85151e26 | + | 3.94163e26i | 0.702135 | + | 0.970556i | ||||
\(459\) | 6.10091e25 | 0.146983 | ||||||||
\(460\) | −1.17598e26 | + | 3.56975e26i | −0.277218 | + | 0.841510i | ||||
\(461\) | − | 7.05245e26i | − | 1.62679i | −0.581713 | − | 0.813394i | \(-0.697617\pi\) | ||
0.581713 | − | 0.813394i | \(-0.302383\pi\) | |||||||
\(462\) | −7.64983e26 | − | 1.05743e27i | −1.72676 | − | 2.38689i | ||||
\(463\) | − | 3.98400e26i | − | 0.880054i | −0.897984 | − | 0.440027i | \(-0.854969\pi\) | ||
0.897984 | − | 0.440027i | \(-0.145031\pi\) | |||||||
\(464\) | 7.02645e25 | − | 9.50722e25i | 0.151899 | − | 0.205529i | ||||
\(465\) | −3.33775e25 | −0.0706193 | ||||||||
\(466\) | 5.18106e25 | − | 3.74816e25i | 0.107290 | − | 0.0776174i | ||||
\(467\) | 7.28398e25 | 0.147639 | 0.0738193 | − | 0.997272i | \(-0.476481\pi\) | ||||
0.0738193 | + | 0.997272i | \(0.476481\pi\) | |||||||
\(468\) | 1.39660e27 | + | 4.60080e26i | 2.77085 | + | 0.912799i | ||||
\(469\) | 1.09988e27i | 2.13608i | ||||||||
\(470\) | −2.98717e26 | + | 2.16102e26i | −0.567912 | + | 0.410848i | ||||
\(471\) | 1.27117e27i | 2.36589i | ||||||||
\(472\) | −8.27324e25 | − | 2.60019e26i | −0.150749 | − | 0.473790i | ||||
\(473\) | 7.71995e25 | 0.137722 | ||||||||
\(474\) | −7.60833e26 | − | 1.05169e27i | −1.32894 | − | 1.83699i | ||||
\(475\) | −6.57288e25 | −0.112414 | ||||||||
\(476\) | 5.86256e25 | + | 1.93130e25i | 0.0981788 | + | 0.0323430i | ||||
\(477\) | − | 2.52481e26i | − | 0.414042i | ||||||
\(478\) | 2.63347e26 | + | 3.64023e26i | 0.422912 | + | 0.584589i | ||||
\(479\) | − | 4.91845e26i | − | 0.773524i | −0.922180 | − | 0.386762i | \(-0.873594\pi\) | ||
0.922180 | − | 0.386762i | \(-0.126406\pi\) | |||||||
\(480\) | 1.23496e25 | − | 1.21267e27i | 0.0190214 | − | 1.86780i | ||||
\(481\) | −8.33881e26 | −1.25792 | ||||||||
\(482\) | −5.29680e26 | + | 3.83190e26i | −0.782607 | + | 0.566165i | ||||
\(483\) | 1.30624e27 | 1.89039 | ||||||||
\(484\) | 1.48226e26 | − | 4.49948e26i | 0.210122 | − | 0.637835i | ||||
\(485\) | − | 9.04251e26i | − | 1.25566i | ||||||
\(486\) | −1.26852e26 | + | 9.17689e25i | −0.172557 | + | 0.124834i | ||||
\(487\) | − | 5.17758e25i | − | 0.0689982i | −0.999405 | − | 0.0344991i | \(-0.989016\pi\) | ||
0.999405 | − | 0.0344991i | \(-0.0109836\pi\) | |||||||
\(488\) | −1.03686e27 | + | 3.29907e26i | −1.35370 | + | 0.430719i | ||||
\(489\) | 1.11868e26 | 0.143092 | ||||||||
\(490\) | 3.48261e26 | + | 4.81399e26i | 0.436460 | + | 0.603315i | ||||
\(491\) | −9.85626e26 | −1.21031 | −0.605156 | − | 0.796107i | \(-0.706889\pi\) | ||||
−0.605156 | + | 0.796107i | \(0.706889\pi\) | |||||||
\(492\) | 1.28352e26 | − | 3.89619e26i | 0.154437 | − | 0.468801i | ||||
\(493\) | − | 1.71987e25i | − | 0.0202780i | ||||||
\(494\) | 5.74943e26 | + | 7.94740e26i | 0.664286 | + | 0.918239i | ||||
\(495\) | 2.51102e27i | 2.84314i | ||||||||
\(496\) | 2.02505e25 | − | 2.74002e25i | 0.0224708 | − | 0.0304044i | ||||
\(497\) | 3.08941e26 | 0.335979 | ||||||||
\(498\) | 1.91191e27 | − | 1.38314e27i | 2.03786 | − | 1.47426i | ||||
\(499\) | −5.61943e26 | −0.587066 | −0.293533 | − | 0.955949i | \(-0.594831\pi\) | ||||
−0.293533 | + | 0.955949i | \(0.594831\pi\) | |||||||
\(500\) | −8.51358e26 | − | 2.80462e26i | −0.871791 | − | 0.287193i | ||||
\(501\) | 1.62844e27i | 1.63453i | ||||||||
\(502\) | −3.35078e26 | + | 2.42407e26i | −0.329692 | + | 0.238511i | ||||
\(503\) | − | 1.05876e27i | − | 1.02121i | −0.859815 | − | 0.510606i | \(-0.829421\pi\) | ||
0.859815 | − | 0.510606i | \(-0.170579\pi\) | |||||||
\(504\) | −2.70348e27 | + | 8.60188e26i | −2.55634 | + | 0.813370i | ||||
\(505\) | 1.34375e27 | 1.24568 | ||||||||
\(506\) | 6.91740e26 | + | 9.56188e26i | 0.628692 | + | 0.869036i | ||||
\(507\) | 1.97704e27 | 1.76172 | ||||||||
\(508\) | 5.45782e26 | + | 1.79796e26i | 0.476850 | + | 0.157088i | ||||
\(509\) | − | 3.14483e26i | − | 0.269414i | −0.990885 | − | 0.134707i | \(-0.956991\pi\) | ||
0.990885 | − | 0.134707i | \(-0.0430093\pi\) | |||||||
\(510\) | −1.03412e26 | − | 1.42945e26i | −0.0868696 | − | 0.120079i | ||||
\(511\) | − | 1.22193e27i | − | 1.00656i | ||||||
\(512\) | 9.88009e26 | + | 7.45878e26i | 0.798107 | + | 0.602515i | ||||
\(513\) | −1.87060e27 | −1.48186 | ||||||||
\(514\) | −1.23773e27 | + | 8.95417e26i | −0.961600 | + | 0.695655i | ||||
\(515\) | −1.86801e27 | −1.42333 | ||||||||
\(516\) | 7.80061e25 | − | 2.36792e26i | 0.0582950 | − | 0.176958i | ||||
\(517\) | 1.15770e27i | 0.848573i | ||||||||
\(518\) | 1.30354e27 | − | 9.43023e26i | 0.937185 | − | 0.677992i | ||||
\(519\) | 1.38383e27i | 0.975907i | ||||||||
\(520\) | −6.63157e26 | − | 2.08423e27i | −0.458757 | − | 1.44183i | ||||
\(521\) | −4.30189e26 | −0.291932 | −0.145966 | − | 0.989290i | \(-0.546629\pi\) | ||||
−0.145966 | + | 0.989290i | \(0.546629\pi\) | |||||||
\(522\) | 4.63338e26 | + | 6.40469e26i | 0.308455 | + | 0.426376i | ||||
\(523\) | 1.17110e27 | 0.764851 | 0.382425 | − | 0.923986i | \(-0.375089\pi\) | ||||
0.382425 | + | 0.923986i | \(0.375089\pi\) | |||||||
\(524\) | 7.77864e26 | − | 2.36125e27i | 0.498415 | − | 1.51297i | ||||
\(525\) | − | 5.09366e26i | − | 0.320211i | ||||||
\(526\) | 2.10264e26 | + | 2.90647e26i | 0.129691 | + | 0.179270i | ||||
\(527\) | − | 4.95672e24i | − | 0.00299977i | ||||||
\(528\) | −3.06241e27 | − | 2.26332e27i | −1.81855 | − | 1.34402i | ||||
\(529\) | 5.34980e26 | 0.311732 | ||||||||
\(530\) | −3.04278e26 | + | 2.20125e26i | −0.173985 | + | 0.125867i | ||||
\(531\) | 1.82455e27 | 1.02379 | ||||||||
\(532\) | −1.79752e27 | − | 5.92155e26i | −0.989822 | − | 0.326076i | ||||
\(533\) | − | 7.39834e26i | − | 0.399818i | ||||||
\(534\) | 2.70351e27 | − | 1.95582e27i | 1.43389 | − | 1.03733i | ||||
\(535\) | 3.11958e27i | 1.62389i | ||||||||
\(536\) | 9.73021e26 | + | 3.05810e27i | 0.497135 | + | 1.56244i | ||||
\(537\) | −1.82071e27 | −0.913055 | ||||||||
\(538\) | −1.54237e27 | − | 2.13201e27i | −0.759218 | − | 1.04946i | ||||
\(539\) | 1.86569e27 | 0.901473 | ||||||||
\(540\) | 3.96159e27 | + | 1.30506e27i | 1.87902 | + | 0.619004i | ||||
\(541\) | − | 1.72051e27i | − | 0.801098i | −0.916275 | − | 0.400549i | \(-0.868819\pi\) | ||
0.916275 | − | 0.400549i | \(-0.131181\pi\) | |||||||
\(542\) | 1.99045e27 | + | 2.75139e27i | 0.909827 | + | 1.25765i | ||||
\(543\) | − | 3.22904e27i | − | 1.44902i | ||||||
\(544\) | 1.80087e26 | + | 1.83398e24i | 0.0793403 | + | 0.000807989i | ||||
\(545\) | −3.33034e27 | −1.44053 | ||||||||
\(546\) | −6.15884e27 | + | 4.45552e27i | −2.61561 | + | 1.89222i | ||||
\(547\) | 4.25552e26 | 0.177451 | 0.0887256 | − | 0.996056i | \(-0.471721\pi\) | ||||
0.0887256 | + | 0.996056i | \(0.471721\pi\) | |||||||
\(548\) | −6.14521e26 | + | 1.86541e27i | −0.251612 | + | 0.763781i | ||||
\(549\) | − | 7.27566e27i | − | 2.92516i | ||||||
\(550\) | 3.72863e26 | − | 2.69742e26i | 0.147205 | − | 0.106493i | ||||
\(551\) | 5.27328e26i | 0.204440i | ||||||||
\(552\) | 3.63186e27 | − | 1.15558e27i | 1.38273 | − | 0.439954i | ||||
\(553\) | 4.51682e27 | 1.68881 | ||||||||
\(554\) | −2.52804e27 | − | 3.49449e27i | −0.928294 | − | 1.28317i | ||||
\(555\) | −4.59870e27 | −1.65846 | ||||||||
\(556\) | −1.36918e27 | + | 4.15621e27i | −0.484966 | + | 1.47214i | ||||
\(557\) | − | 4.34136e26i | − | 0.151034i | −0.997145 | − | 0.0755168i | \(-0.975939\pi\) | ||
0.997145 | − | 0.0755168i | \(-0.0240606\pi\) | |||||||
\(558\) | 1.33536e26 | + | 1.84585e26i | 0.0456305 | + | 0.0630747i | ||||
\(559\) | − | 4.49636e26i | − | 0.150919i | ||||||
\(560\) | 3.39369e27 | + | 2.50815e27i | 1.11890 | + | 0.826940i | ||||
\(561\) | −5.53994e26 | −0.179422 | ||||||||
\(562\) | 3.67451e27 | − | 2.65827e27i | 1.16906 | − | 0.845738i | ||||
\(563\) | 2.52994e27 | 0.790726 | 0.395363 | − | 0.918525i | \(-0.370619\pi\) | ||||
0.395363 | + | 0.918525i | \(0.370619\pi\) | |||||||
\(564\) | 3.55097e27 | + | 1.16979e27i | 1.09033 | + | 0.359185i | ||||
\(565\) | 2.45524e27i | 0.740643i | ||||||||
\(566\) | 1.19763e27 | − | 8.66409e26i | 0.354943 | − | 0.256778i | ||||
\(567\) | − | 5.28347e27i | − | 1.53847i | ||||||
\(568\) | 8.58975e26 | − | 2.73307e26i | 0.245752 | − | 0.0781929i | ||||
\(569\) | −7.02287e26 | −0.197420 | −0.0987102 | − | 0.995116i | \(-0.531472\pi\) | ||||
−0.0987102 | + | 0.995116i | \(0.531472\pi\) | |||||||
\(570\) | 3.17070e27 | + | 4.38284e27i | 0.875804 | + | 1.21062i | ||||
\(571\) | −5.41269e27 | −1.46910 | −0.734551 | − | 0.678554i | \(-0.762607\pi\) | ||||
−0.734551 | + | 0.678554i | \(0.762607\pi\) | |||||||
\(572\) | −6.52302e27 | − | 2.14887e27i | −1.73976 | − | 0.573126i | ||||
\(573\) | 8.26897e27i | 2.16723i | ||||||||
\(574\) | 8.36668e26 | + | 1.15652e27i | 0.215493 | + | 0.297875i | ||||
\(575\) | 4.60597e26i | 0.116585i | ||||||||
\(576\) | −6.75576e27 | + | 4.78331e27i | −1.68054 | + | 1.18988i | ||||
\(577\) | −6.96493e27 | −1.70278 | −0.851390 | − | 0.524533i | \(-0.824240\pi\) | ||||
−0.851390 | + | 0.524533i | \(0.824240\pi\) | |||||||
\(578\) | −3.35069e27 | + | 2.42401e27i | −0.805112 | + | 0.582446i | ||||
\(579\) | −4.92163e26 | −0.116231 | ||||||||
\(580\) | 3.67901e26 | − | 1.11678e27i | 0.0853987 | − | 0.259233i | ||||
\(581\) | 8.21127e27i | 1.87348i | ||||||||
\(582\) | −7.42928e27 | + | 5.37460e27i | −1.66616 | + | 1.20536i | ||||
\(583\) | 1.17925e27i | 0.259968i | ||||||||
\(584\) | −1.08099e27 | − | 3.39744e27i | −0.234258 | − | 0.736247i | ||||
\(585\) | 1.46250e28 | 3.11558 | ||||||||
\(586\) | −5.34237e27 | − | 7.38472e27i | −1.11881 | − | 1.54653i | ||||
\(587\) | 1.18193e27 | 0.243339 | 0.121670 | − | 0.992571i | \(-0.461175\pi\) | ||||
0.121670 | + | 0.992571i | \(0.461175\pi\) | |||||||
\(588\) | 1.88519e27 | − | 5.72259e27i | 0.381576 | − | 1.15830i | ||||
\(589\) | 1.51978e26i | 0.0302432i | ||||||||
\(590\) | −1.59074e27 | − | 2.19886e27i | −0.311227 | − | 0.430208i | ||||
\(591\) | 3.71152e27i | 0.713965i | ||||||||
\(592\) | 2.79008e27 | − | 3.77515e27i | 0.527715 | − | 0.714032i | ||||
\(593\) | 7.11802e27 | 1.32377 | 0.661885 | − | 0.749605i | \(-0.269757\pi\) | ||||
0.661885 | + | 0.749605i | \(0.269757\pi\) | |||||||
\(594\) | 1.06114e28 | − | 7.67670e27i | 1.94048 | − | 1.40381i | ||||
\(595\) | 6.13922e26 | 0.110393 | ||||||||
\(596\) | 4.62037e27 | + | 1.52208e27i | 0.816984 | + | 0.269138i | ||||
\(597\) | 1.72223e27i | 0.299466i | ||||||||
\(598\) | 5.56917e27 | − | 4.02893e27i | 0.952310 | − | 0.688935i | ||||
\(599\) | − | 6.82077e27i | − | 1.14701i | −0.819204 | − | 0.573503i | \(-0.805584\pi\) | ||
0.819204 | − | 0.573503i | \(-0.194416\pi\) | |||||||
\(600\) | −4.50614e26 | − | 1.41623e27i | −0.0745233 | − | 0.234219i | ||||
\(601\) | 9.85205e27 | 1.60244 | 0.801220 | − | 0.598370i | \(-0.204185\pi\) | ||||
0.801220 | + | 0.598370i | \(0.204185\pi\) | |||||||
\(602\) | 5.08487e26 | + | 7.02878e26i | 0.0813420 | + | 0.112439i | ||||
\(603\) | −2.14587e28 | −3.37621 | ||||||||
\(604\) | 6.53306e27 | + | 2.15218e27i | 1.01099 | + | 0.333050i | ||||
\(605\) | − | 4.71181e27i | − | 0.717190i | ||||||
\(606\) | −7.98688e27 | − | 1.10402e28i | −1.19578 | − | 1.65292i | ||||
\(607\) | − | 5.11586e25i | − | 0.00753411i | −0.999993 | − | 0.00376706i | \(-0.998801\pi\) | ||
0.999993 | − | 0.00376706i | \(-0.00119909\pi\) | |||||||
\(608\) | −5.52166e27 | − | 5.62317e25i | −0.799896 | − | 0.00814601i | ||||
\(609\) | −4.08653e27 | −0.582347 | ||||||||
\(610\) | −8.76828e27 | + | 6.34328e27i | −1.22918 | + | 0.889233i | ||||
\(611\) | 6.74282e27 | 0.929886 | ||||||||
\(612\) | −3.76795e26 | + | 1.14378e27i | −0.0511200 | + | 0.155178i | ||||
\(613\) | − | 1.04122e28i | − | 1.38976i | −0.719126 | − | 0.694880i | \(-0.755458\pi\) | ||
0.719126 | − | 0.694880i | \(-0.244542\pi\) | |||||||
\(614\) | 6.89221e26 | − | 4.98607e26i | 0.0905055 | − | 0.0654749i | ||||
\(615\) | − | 4.08005e27i | − | 0.527126i | ||||||
\(616\) | 1.26270e28 | − | 4.01764e27i | 1.60507 | − | 0.510697i | ||||
\(617\) | −8.77445e27 | −1.09741 | −0.548704 | − | 0.836017i | \(-0.684879\pi\) | ||||
−0.548704 | + | 0.836017i | \(0.684879\pi\) | |||||||
\(618\) | 1.11029e28 | + | 1.53475e28i | 1.36632 | + | 1.88865i | ||||
\(619\) | 8.64119e27 | 1.04633 | 0.523163 | − | 0.852233i | \(-0.324752\pi\) | ||||
0.523163 | + | 0.852233i | \(0.324752\pi\) | |||||||
\(620\) | 1.06030e26 | − | 3.21861e26i | 0.0126332 | − | 0.0383488i | ||||
\(621\) | 1.31083e28i | 1.53684i | ||||||||
\(622\) | −6.07003e27 | − | 8.39056e27i | −0.700304 | − | 0.968026i | ||||
\(623\) | 1.16110e28i | 1.31823i | ||||||||
\(624\) | −1.31824e28 | + | 1.78366e28i | −1.47281 | + | 1.99281i | ||||
\(625\) | −1.01934e28 | −1.12078 | ||||||||
\(626\) | 5.19115e27 | − | 3.75546e27i | 0.561720 | − | 0.406368i | ||||
\(627\) | 1.69860e28 | 1.80890 | ||||||||
\(628\) | −1.22580e28 | − | 4.03814e27i | −1.28476 | − | 0.423238i | ||||
\(629\) | − | 6.82929e26i | − | 0.0704481i | ||||||
\(630\) | −2.28621e28 | + | 1.65393e28i | −2.32119 | + | 1.67923i | ||||
\(631\) | 2.44535e27i | 0.244369i | 0.992507 | + | 0.122185i | \(0.0389900\pi\) | ||||
−0.992507 | + | 0.122185i | \(0.961010\pi\) | |||||||
\(632\) | 1.25585e28 | − | 3.99584e27i | 1.23529 | − | 0.393040i | ||||
\(633\) | −6.01163e27 | −0.582044 | ||||||||
\(634\) | −3.81980e27 | − | 5.28008e27i | −0.364039 | − | 0.503209i | ||||
\(635\) | 5.71537e27 | 0.536176 | ||||||||
\(636\) | 3.61707e27 | + | 1.19157e27i | 0.334031 | + | 0.110039i | ||||
\(637\) | − | 1.08664e28i | − | 0.987855i | ||||||
\(638\) | −2.16409e27 | − | 2.99140e27i | −0.193672 | − | 0.267712i | ||||
\(639\) | 6.02742e27i | 0.531035i | ||||||||
\(640\) | 1.16546e28 | + | 3.97139e27i | 1.01088 | + | 0.344463i | ||||
\(641\) | −5.88668e27 | −0.502678 | −0.251339 | − | 0.967899i | \(-0.580871\pi\) | ||||
−0.251339 | + | 0.967899i | \(0.580871\pi\) | |||||||
\(642\) | 2.56303e28 | − | 1.85418e28i | 2.15478 | − | 1.55884i | ||||
\(643\) | −6.70815e27 | −0.555256 | −0.277628 | − | 0.960689i | \(-0.589548\pi\) | ||||
−0.277628 | + | 0.960689i | \(0.589548\pi\) | |||||||
\(644\) | −4.14955e27 | + | 1.25962e28i | −0.338175 | + | 1.02655i | ||||
\(645\) | − | 2.47966e27i | − | 0.198973i | ||||||
\(646\) | −6.50874e26 | + | 4.70865e26i | −0.0514247 | + | 0.0372024i | ||||
\(647\) | 4.12884e27i | 0.321207i | 0.987019 | + | 0.160604i | \(0.0513441\pi\) | ||||
−0.987019 | + | 0.160604i | \(0.948656\pi\) | |||||||
\(648\) | −4.67406e27 | − | 1.46901e28i | −0.358050 | − | 1.12532i | ||||
\(649\) | −8.52184e27 | −0.642816 | ||||||||
\(650\) | −1.57107e27 | − | 2.17168e27i | −0.116698 | − | 0.161311i | ||||
\(651\) | −1.17775e27 | −0.0861478 | ||||||||
\(652\) | −3.55371e26 | + | 1.07875e27i | −0.0255980 | + | 0.0777042i | ||||
\(653\) | 9.05389e27i | 0.642249i | 0.947037 | + | 0.321124i | \(0.104061\pi\) | ||||
−0.947037 | + | 0.321124i | \(0.895939\pi\) | |||||||
\(654\) | 1.97946e28 | + | 2.73619e28i | 1.38283 | + | 1.91147i | ||||
\(655\) | − | 2.47268e28i | − | 1.70120i | ||||||
\(656\) | 3.34939e27 | + | 2.47541e27i | 0.226948 | + | 0.167729i | ||||
\(657\) | 2.38398e28 | 1.59092 | ||||||||
\(658\) | −1.05405e28 | + | 7.62536e27i | −0.692790 | + | 0.501189i | ||||
\(659\) | −9.80711e27 | −0.634873 | −0.317436 | − | 0.948280i | \(-0.602822\pi\) | ||||
−0.317436 | + | 0.948280i | \(0.602822\pi\) | |||||||
\(660\) | −3.59732e28 | − | 1.18506e28i | −2.29372 | − | 0.755618i | ||||
\(661\) | 4.81270e27i | 0.302256i | 0.988514 | + | 0.151128i | \(0.0482905\pi\) | ||||
−0.988514 | + | 0.151128i | \(0.951709\pi\) | |||||||
\(662\) | 1.00861e28 | − | 7.29662e27i | 0.623939 | − | 0.451379i | ||||
\(663\) | 3.22665e27i | 0.196615i | ||||||||
\(664\) | 7.26416e27 | + | 2.28305e28i | 0.436018 | + | 1.37036i | ||||
\(665\) | −1.88235e28 | −1.11297 | ||||||||
\(666\) | 1.83983e28 | + | 2.54319e28i | 1.07161 | + | 1.48128i | ||||
\(667\) | 3.69527e27 | 0.212025 | ||||||||
\(668\) | −1.57031e28 | − | 5.17307e27i | −0.887609 | − | 0.292404i | ||||
\(669\) | − | 5.20958e28i | − | 2.90096i | ||||||
\(670\) | 1.87087e28 | + | 2.58610e28i | 1.02635 | + | 1.41872i | ||||
\(671\) | 3.39820e28i | 1.83664i | ||||||||
\(672\) | 4.35768e26 | − | 4.27901e28i | 0.0232040 | − | 2.27851i | ||||
\(673\) | 2.49736e28 | 1.31018 | 0.655089 | − | 0.755551i | \(-0.272631\pi\) | ||||
0.655089 | + | 0.755551i | \(0.272631\pi\) | |||||||
\(674\) | −2.74610e28 | + | 1.98663e28i | −1.41944 | + | 1.02688i | ||||
\(675\) | 5.11154e27 | 0.260324 | ||||||||
\(676\) | −6.28049e27 | + | 1.90648e28i | −0.315157 | + | 0.956675i | ||||
\(677\) | − | 3.55953e28i | − | 1.75997i | −0.475000 | − | 0.879986i | \(-0.657552\pi\) | ||
0.475000 | − | 0.879986i | \(-0.342448\pi\) | |||||||
\(678\) | 2.01721e28 | − | 1.45932e28i | 0.982776 | − | 0.710975i | ||||
\(679\) | − | 3.19073e28i | − | 1.53177i | ||||||
\(680\) | 1.70694e27 | − | 5.43111e26i | 0.0807475 | − | 0.0256921i | ||||
\(681\) | −4.18737e28 | −1.95196 | ||||||||
\(682\) | −6.23697e26 | − | 8.62133e26i | −0.0286504 | − | 0.0396032i | ||||
\(683\) | −1.29451e28 | −0.586003 | −0.293002 | − | 0.956112i | \(-0.594654\pi\) | ||||
−0.293002 | + | 0.956112i | \(0.594654\pi\) | |||||||
\(684\) | 1.15529e28 | − | 3.50695e28i | 0.515384 | − | 1.56447i | ||||
\(685\) | 1.95344e28i | 0.858805i | ||||||||
\(686\) | −5.33566e27 | − | 7.37546e27i | −0.231178 | − | 0.319557i | ||||
\(687\) | − | 4.90669e28i | − | 2.09518i | ||||||
\(688\) | 2.03560e27 | + | 1.50444e27i | 0.0856658 | + | 0.0633125i | ||||
\(689\) | 6.86834e27 | 0.284879 | ||||||||
\(690\) | 3.07129e28 | − | 2.22188e28i | 1.25554 | − | 0.908301i | ||||
\(691\) | 3.30931e28 | 1.33339 | 0.666694 | − | 0.745331i | \(-0.267709\pi\) | ||||
0.666694 | + | 0.745331i | \(0.267709\pi\) | |||||||
\(692\) | −1.33444e28 | − | 4.39602e27i | −0.529952 | − | 0.174582i | ||||
\(693\) | 8.86036e28i | 3.46832i | ||||||||
\(694\) | −1.07197e28 | + | 7.75503e27i | −0.413608 | + | 0.299219i | ||||
\(695\) | 4.35234e28i | 1.65529i | ||||||||
\(696\) | −1.13621e28 | + | 3.61518e27i | −0.425959 | + | 0.135531i | ||||
\(697\) | 6.05907e26 | 0.0223912 | ||||||||
\(698\) | −9.13275e27 | − | 1.26241e28i | −0.332696 | − | 0.459883i | ||||
\(699\) | −6.44958e27 | −0.231611 | ||||||||
\(700\) | 4.91185e27 | + | 1.61811e27i | 0.173886 | + | 0.0572831i | ||||
\(701\) | 1.27653e27i | 0.0445502i | 0.999752 | + | 0.0222751i | \(0.00709098\pi\) | ||||
−0.999752 | + | 0.0222751i | \(0.992909\pi\) | |||||||
\(702\) | −4.47117e28 | − | 6.18047e28i | −1.53833 | − | 2.12643i | ||||
\(703\) | 2.09393e28i | 0.710246i | ||||||||
\(704\) | 3.15538e28 | − | 2.23412e28i | 1.05518 | − | 0.747101i | ||||
\(705\) | 3.71854e28 | 1.22597 | ||||||||
\(706\) | 9.55634e26 | − | 6.91339e26i | 0.0310631 | − | 0.0224721i | ||||
\(707\) | 4.74156e28 | 1.51959 | ||||||||
\(708\) | −8.61088e27 | + | 2.61388e28i | −0.272092 | + | 0.825949i | ||||
\(709\) | 5.44035e27i | 0.169498i | 0.996402 | + | 0.0847490i | \(0.0270089\pi\) | ||||
−0.996402 | + | 0.0847490i | \(0.972991\pi\) | |||||||
\(710\) | 7.26396e27 | − | 5.25500e27i | 0.223146 | − | 0.161432i | ||||
\(711\) | 8.81229e28i | 2.66927i | ||||||||
\(712\) | 1.02718e28 | + | 3.22832e28i | 0.306794 | + | 0.964222i | ||||
\(713\) | 1.06499e27 | 0.0313653 | ||||||||
\(714\) | −3.64897e27 | − | 5.04395e27i | −0.105971 | − | 0.146483i | ||||
\(715\) | −6.83084e28 | −1.95620 | ||||||||
\(716\) | 5.78385e27 | − | 1.75572e28i | 0.163338 | − | 0.495821i | ||||
\(717\) | − | 4.53150e28i | − | 1.26198i | ||||||
\(718\) | −9.75461e27 | − | 1.34837e28i | −0.267895 | − | 0.370310i | ||||
\(719\) | − | 2.02337e27i | − | 0.0548008i | −0.999625 | − | 0.0274004i | \(-0.991277\pi\) | ||
0.999625 | − | 0.0274004i | \(-0.00872291\pi\) | |||||||
\(720\) | −4.89339e28 | + | 6.62107e28i | −1.30703 | + | 1.76849i | ||||
\(721\) | −6.59143e28 | −1.73631 | ||||||||
\(722\) | −1.12304e28 | + | 8.12445e27i | −0.291758 | + | 0.211068i | ||||
\(723\) | 6.59367e28 | 1.68944 | ||||||||
\(724\) | 3.11379e28 | + | 1.02577e28i | 0.786872 | + | 0.259218i | ||||
\(725\) | − | 1.44096e27i | − | 0.0359147i | ||||||
\(726\) | −3.87120e28 | + | 2.80056e28i | −0.951655 | + | 0.688461i | ||||
\(727\) | − | 9.01083e26i | − | 0.0218485i | −0.999940 | − | 0.0109242i | \(-0.996523\pi\) | ||
0.999940 | − | 0.0109242i | \(-0.00347736\pi\) | |||||||
\(728\) | −2.34001e28 | − | 7.35441e28i | −0.559634 | − | 1.75887i | ||||
\(729\) | −3.42689e28 | −0.808398 | ||||||||
\(730\) | −2.07847e28 | − | 2.87306e28i | −0.483633 | − | 0.668523i | ||||
\(731\) | 3.68242e26 | 0.00845200 | ||||||||
\(732\) | 1.04232e29 | + | 3.43371e28i | 2.35989 | + | 0.777415i | ||||
\(733\) | 6.55566e28i | 1.46412i | 0.681240 | + | 0.732060i | \(0.261441\pi\) | ||||
−0.681240 | + | 0.732060i | \(0.738559\pi\) | |||||||
\(734\) | 1.11742e28 | + | 1.54461e28i | 0.246182 | + | 0.340296i | ||||
\(735\) | − | 5.99264e28i | − | 1.30240i | ||||||
\(736\) | −3.94045e26 | + | 3.86932e28i | −0.00844827 | + | 0.829576i | ||||
\(737\) | 1.00226e29 | 2.11985 | ||||||||
\(738\) | −2.25636e28 | + | 1.63233e28i | −0.470810 | + | 0.340601i | ||||
\(739\) | −6.04226e28 | −1.24381 | −0.621907 | − | 0.783091i | \(-0.713642\pi\) | ||||
−0.621907 | + | 0.783091i | \(0.713642\pi\) | |||||||
\(740\) | 1.46087e28 | − | 4.43456e28i | 0.296685 | − | 0.900602i | ||||
\(741\) | − | 9.89323e28i | − | 1.98224i | ||||||
\(742\) | −1.07367e28 | + | 7.76731e27i | −0.212242 | + | 0.153544i | ||||
\(743\) | − | 9.90525e28i | − | 1.93187i | −0.258790 | − | 0.965934i | \(-0.583324\pi\) | ||
0.258790 | − | 0.965934i | \(-0.416676\pi\) | |||||||
\(744\) | −3.27461e27 | + | 1.04191e27i | −0.0630130 | + | 0.0200493i | ||||
\(745\) | 4.83840e28 | 0.918627 | ||||||||
\(746\) | −5.10694e27 | − | 7.05928e27i | −0.0956692 | − | 0.132243i | ||||
\(747\) | −1.60201e29 | −2.96115 | ||||||||
\(748\) | 1.75988e27 | − | 5.34220e27i | 0.0320971 | − | 0.0974326i | ||||
\(749\) | 1.10077e29i | 1.98097i | ||||||||
\(750\) | 5.29902e28 | + | 7.32480e28i | 0.940985 | + | 1.30072i | ||||
\(751\) | − | 4.87745e27i | − | 0.0854661i | −0.999087 | − | 0.0427330i | \(-0.986394\pi\) | ||
0.999087 | − | 0.0427330i | \(-0.0136065\pi\) | |||||||
\(752\) | −2.25608e28 | + | 3.05262e28i | −0.390100 | + | 0.527830i | ||||
\(753\) | 4.17118e28 | 0.711720 | ||||||||
\(754\) | −1.74230e28 | + | 1.26044e28i | −0.293365 | + | 0.212231i | ||||
\(755\) | 6.84136e28 | 1.13677 | ||||||||
\(756\) | 1.39788e29 | + | 4.60503e28i | 2.29220 | + | 0.755117i | ||||
\(757\) | − | 3.69662e28i | − | 0.598199i | −0.954222 | − | 0.299099i | \(-0.903314\pi\) | ||
0.954222 | − | 0.299099i | \(-0.0966862\pi\) | |||||||
\(758\) | 6.48748e28 | − | 4.69328e28i | 1.03606 | − | 0.749521i | ||||
\(759\) | − | 1.19030e29i | − | 1.87602i | ||||||
\(760\) | −5.23365e28 | + | 1.66523e28i | −0.814083 | + | 0.259023i | ||||
\(761\) | 1.38381e28 | 0.212437 | 0.106219 | − | 0.994343i | \(-0.466126\pi\) | ||||
0.106219 | + | 0.994343i | \(0.466126\pi\) | |||||||
\(762\) | −3.39705e28 | − | 4.69572e28i | −0.514698 | − | 0.711463i | ||||
\(763\) | −1.17514e29 | −1.75729 | ||||||||
\(764\) | −7.97383e28 | − | 2.62681e28i | −1.17688 | − | 0.387700i | ||||
\(765\) | 1.19776e28i | 0.174484i | ||||||||
\(766\) | −3.35444e28 | − | 4.63682e28i | −0.482317 | − | 0.666704i | ||||
\(767\) | 4.96341e28i | 0.704412i | ||||||||
\(768\) | −3.66430e28 | − | 1.19359e29i | −0.513309 | − | 1.67202i | ||||
\(769\) | 1.30708e29 | 1.80733 | 0.903665 | − | 0.428240i | \(-0.140866\pi\) | ||||
0.903665 | + | 0.428240i | \(0.140866\pi\) | |||||||
\(770\) | 1.06781e29 | − | 7.72490e28i | 1.45742 | − | 1.05435i | ||||
\(771\) | 1.54077e29 | 2.07584 | ||||||||
\(772\) | 1.56346e27 | − | 4.74597e27i | 0.0207928 | − | 0.0631178i | ||||
\(773\) | 2.16151e28i | 0.283767i | 0.989883 | + | 0.141883i | \(0.0453158\pi\) | ||||
−0.989883 | + | 0.141883i | \(0.954684\pi\) | |||||||
\(774\) | −1.37131e28 | + | 9.92055e27i | −0.177716 | + | 0.128566i | ||||
\(775\) | − | 4.15290e26i | − | 0.00531294i | ||||||
\(776\) | −2.82270e28 | − | 8.87147e28i | −0.356491 | − | 1.12041i | ||||
\(777\) | −1.62269e29 | −2.02314 | ||||||||
\(778\) | 6.53241e28 | + | 9.02971e28i | 0.804039 | + | 1.11142i | ||||
\(779\) | −1.85777e28 | −0.225745 | ||||||||
\(780\) | −6.90222e28 | + | 2.09521e29i | −0.828023 | + | 2.51351i | ||||
\(781\) | − | 2.81519e28i | − | 0.333425i | ||||||
\(782\) | 3.29960e27 | + | 4.56102e27i | 0.0385828 | + | 0.0533328i | ||||
\(783\) | − | 4.10088e28i | − | 0.473434i | ||||||
\(784\) | 4.91947e28 | + | 3.63580e28i | 0.560735 | + | 0.414419i | ||||
\(785\) | −1.28364e29 | −1.44460 | ||||||||
\(786\) | −2.03154e29 | + | 1.46969e29i | −2.25735 | + | 1.63305i | ||||
\(787\) | −5.25629e28 | −0.576676 | −0.288338 | − | 0.957529i | \(-0.593103\pi\) | ||||
−0.288338 | + | 0.957529i | \(0.593103\pi\) | |||||||
\(788\) | −3.57904e28 | − | 1.17904e28i | −0.387708 | − | 0.127722i | ||||
\(789\) | − | 3.61809e28i | − | 0.386998i | ||||||
\(790\) | 1.06201e29 | − | 7.68299e28i | 1.12166 | − | 0.811445i | ||||
\(791\) | 8.66353e28i | 0.903504i | ||||||||
\(792\) | 7.83838e28 | + | 2.46352e29i | 0.807188 | + | 2.53691i | ||||
\(793\) | 1.97923e29 | 2.01263 | ||||||||
\(794\) | −3.96099e28 | − | 5.47526e28i | −0.397740 | − | 0.549793i | ||||
\(795\) | 3.78776e28 | 0.375588 | ||||||||
\(796\) | −1.66076e28 | − | 5.47103e27i | −0.162621 | − | 0.0535720i | ||||
\(797\) | 2.65924e28i | 0.257143i | 0.991700 | + | 0.128572i | \(0.0410392\pi\) | ||||
−0.991700 | + | 0.128572i | \(0.958961\pi\) | |||||||
\(798\) | 1.11881e29 | + | 1.54653e29i | 1.06838 | + | 1.47682i | ||||
\(799\) | 5.52222e27i | 0.0520770i | ||||||||
\(800\) | 1.50883e28 | + | 1.53657e26i | 0.140521 | + | 0.00143104i | ||||
\(801\) | −2.26531e29 | −2.08354 | ||||||||
\(802\) | −1.34173e29 | + | 9.70655e28i | −1.21877 | + | 0.881701i | ||||
\(803\) | −1.11347e29 | −0.998906 | ||||||||
\(804\) | 1.01273e29 | − | 3.07420e29i | 0.897292 | − | 2.72378i | ||||
\(805\) | 1.31906e29i | 1.15427i | ||||||||
\(806\) | −5.02136e27 | + | 3.63263e27i | −0.0433981 | + | 0.0313957i | ||||
\(807\) | 2.65401e29i | 2.26552i | ||||||||
\(808\) | 1.31834e29 | − | 4.19466e28i | 1.11151 | − | 0.353657i | ||||
\(809\) | −6.06389e28 | −0.504971 | −0.252486 | − | 0.967601i | \(-0.581248\pi\) | ||||
−0.252486 | + | 0.967601i | \(0.581248\pi\) | |||||||
\(810\) | −8.98704e28 | − | 1.24227e29i | −0.739207 | − | 1.02180i | ||||
\(811\) | 9.14665e28 | 0.743111 | 0.371555 | − | 0.928411i | \(-0.378825\pi\) | ||||
0.371555 | + | 0.928411i | \(0.378825\pi\) | |||||||
\(812\) | 1.29817e28 | − | 3.94067e28i | 0.104177 | − | 0.316235i | ||||
\(813\) | − | 3.42504e29i | − | 2.71494i | ||||||
\(814\) | −8.59321e28 | − | 1.18783e29i | −0.672839 | − | 0.930061i | ||||
\(815\) | 1.12966e28i | 0.0873715i | ||||||||
\(816\) | −1.46077e28 | − | 1.07960e28i | −0.111604 | − | 0.0824827i | ||||
\(817\) | −1.12907e28 | −0.0852116 | ||||||||
\(818\) | −3.82827e28 | + | 2.76950e28i | −0.285410 | + | 0.206476i | ||||
\(819\) | 5.16058e29 | 3.80066 | ||||||||
\(820\) | 3.93442e28 | + | 1.29611e28i | 0.286248 | + | 0.0942984i | ||||
\(821\) | − | 6.45589e27i | − | 0.0464007i | −0.999731 | − | 0.0232003i | \(-0.992614\pi\) | ||
0.999731 | − | 0.0232003i | \(-0.00738556\pi\) | |||||||
\(822\) | 1.60494e29 | − | 1.16107e29i | 1.13957 | − | 0.824403i | ||||
\(823\) | − | 2.13797e29i | − | 1.49969i | −0.661611 | − | 0.749847i | \(-0.730127\pi\) | ||
0.661611 | − | 0.749847i | \(-0.269873\pi\) | |||||||
\(824\) | −1.83267e29 | + | 5.83116e28i | −1.27003 | + | 0.404095i | ||||
\(825\) | −4.64154e28 | −0.317777 | ||||||||
\(826\) | −5.61305e28 | − | 7.75889e28i | −0.379663 | − | 0.524806i | ||||
\(827\) | 1.80939e29 | 1.20914 | 0.604570 | − | 0.796552i | \(-0.293345\pi\) | ||||
0.604570 | + | 0.796552i | \(0.293345\pi\) | |||||||
\(828\) | −2.45751e29 | − | 8.09574e28i | −1.62252 | − | 0.534507i | ||||
\(829\) | 5.97895e28i | 0.390014i | 0.980802 | + | 0.195007i | \(0.0624729\pi\) | ||||
−0.980802 | + | 0.195007i | \(0.937527\pi\) | |||||||
\(830\) | 1.39672e29 | + | 1.93067e29i | 0.900175 | + | 1.24431i | ||||
\(831\) | 4.35007e29i | 2.77004i | ||||||||
\(832\) | −1.30123e29 | − | 1.83780e29i | −0.818690 | − | 1.15629i | ||||
\(833\) | 8.89937e27 | 0.0553234 | ||||||||
\(834\) | 3.57586e29 | − | 2.58690e29i | 2.19644 | − | 1.58898i | ||||
\(835\) | −1.64442e29 | −0.998038 | ||||||||
\(836\) | −5.39596e28 | + | 1.63797e29i | −0.323598 | + | 0.982299i | ||||
\(837\) | − | 1.18189e28i | − | 0.0700361i | ||||||
\(838\) | −4.39407e27 | + | 3.17883e27i | −0.0257293 | + | 0.0186135i | ||||
\(839\) | 2.02650e29i | 1.17254i | 0.810116 | + | 0.586270i | \(0.199404\pi\) | ||||
−0.810116 | + | 0.586270i | \(0.800596\pi\) | |||||||
\(840\) | −1.29047e29 | − | 4.05582e29i | −0.737829 | − | 2.31892i | ||||
\(841\) | 1.65434e29 | 0.934684 | ||||||||
\(842\) | 8.96508e28 | + | 1.23924e29i | 0.500534 | + | 0.691884i | ||||
\(843\) | −4.57417e29 | −2.52369 | ||||||||
\(844\) | 1.90972e28 | − | 5.79706e28i | 0.104123 | − | 0.316070i | ||||
\(845\) | 1.99644e29i | 1.07570i | ||||||||
\(846\) | −1.48770e29 | − | 2.05644e29i | −0.792160 | − | 1.09500i | ||||
\(847\) | − | 1.66260e29i | − | 0.874893i | ||||||
\(848\) | −2.29808e28 | + | 3.10944e28i | −0.119511 | + | 0.161705i | ||||
\(849\) | −1.49086e29 | −0.766230 | ||||||||
\(850\) | 1.77856e27 | − | 1.28667e27i | 0.00903398 | − | 0.00653550i | ||||
\(851\) | 1.46733e29 | 0.736599 | ||||||||
\(852\) | −8.63497e28 | − | 2.84461e28i | −0.428415 | − | 0.141132i | ||||
\(853\) | 2.56218e29i | 1.25637i | 0.778063 | + | 0.628187i | \(0.216203\pi\) | ||||
−0.778063 | + | 0.628187i | \(0.783797\pi\) | |||||||
\(854\) | −3.09397e29 | + | 2.23828e29i | −1.49947 | + | 1.08477i | ||||
\(855\) | − | 3.67244e29i | − | 1.75911i | ||||||
\(856\) | 9.73805e28 | + | 3.06057e29i | 0.461035 | + | 1.44899i | ||||
\(857\) | −3.98633e27 | −0.0186537 | −0.00932685 | − | 0.999957i | \(-0.502969\pi\) | ||||
−0.00932685 | + | 0.999957i | \(0.502969\pi\) | |||||||
\(858\) | 4.06005e29 | + | 5.61219e29i | 1.87784 | + | 2.59573i | ||||
\(859\) | −1.87586e29 | −0.857568 | −0.428784 | − | 0.903407i | \(-0.641058\pi\) | ||||
−0.428784 | + | 0.903407i | \(0.641058\pi\) | |||||||
\(860\) | 2.39116e28 | + | 7.87716e27i | 0.108050 | + | 0.0355947i | ||||
\(861\) | − | 1.43968e29i | − | 0.643035i | ||||||
\(862\) | 3.46146e28 | + | 4.78475e28i | 0.152822 | + | 0.211245i | ||||
\(863\) | − | 4.00633e29i | − | 1.74839i | −0.485572 | − | 0.874197i | \(-0.661389\pi\) | ||
0.485572 | − | 0.874197i | \(-0.338611\pi\) | |||||||
\(864\) | 4.29404e29 | + | 4.37298e27i | 1.85237 | + | 0.0188643i | ||||
\(865\) | −1.39741e29 | −0.595885 | ||||||||
\(866\) | 3.00626e29 | − | 2.17484e29i | 1.26721 | − | 0.916744i | ||||
\(867\) | 4.17107e29 | 1.73803 | ||||||||
\(868\) | 3.74138e27 | − | 1.13572e28i | 0.0154111 | − | 0.0467813i | ||||
\(869\) | − | 4.11591e29i | − | 1.67598i | ||||||
\(870\) | −9.60844e28 | + | 6.95108e28i | −0.386777 | + | 0.279808i | ||||
\(871\) | − | 5.83750e29i | − | 2.32298i | ||||||
\(872\) | −3.26734e29 | + | 1.03960e29i | −1.28538 | + | 0.408978i | ||||
\(873\) | 6.22509e29 | 2.42105 | ||||||||
\(874\) | −1.01169e29 | − | 1.39845e29i | −0.388986 | − | 0.537692i | ||||
\(875\) | −3.14586e29 | −1.19580 | ||||||||
\(876\) | −1.12511e29 | + | 3.41533e29i | −0.422818 | + | 1.28349i | ||||
\(877\) | − | 2.28056e29i | − | 0.847317i | −0.905822 | − | 0.423659i | \(-0.860746\pi\) | ||
0.905822 | − | 0.423659i | \(-0.139254\pi\) | |||||||
\(878\) | 1.21258e29 | + | 1.67615e29i | 0.445417 | + | 0.615697i | ||||
\(879\) | 9.19279e29i | 3.33855i | ||||||||
\(880\) | 2.28553e29 | − | 3.09247e29i | 0.820654 | − | 1.11040i | ||||
\(881\) | −4.46767e29 | −1.58607 | −0.793034 | − | 0.609178i | \(-0.791500\pi\) | ||||
−0.793034 | + | 0.609178i | \(0.791500\pi\) | |||||||
\(882\) | −3.31407e29 | + | 2.39752e29i | −1.16326 | + | 0.841543i | ||||
\(883\) | 1.24718e29 | 0.432835 | 0.216418 | − | 0.976301i | \(-0.430563\pi\) | ||||
0.216418 | + | 0.976301i | \(0.430563\pi\) | |||||||
\(884\) | −3.11148e28 | − | 1.02501e28i | −0.106769 | − | 0.0351728i | ||||
\(885\) | 2.73723e29i | 0.928707i | ||||||||
\(886\) | −4.29202e29 | + | 3.10500e29i | −1.43987 | + | 1.04166i | ||||
\(887\) | 4.57913e29i | 1.51896i | 0.650530 | + | 0.759481i | \(0.274547\pi\) | ||||
−0.650530 | + | 0.759481i | \(0.725453\pi\) | |||||||
\(888\) | −4.51171e29 | + | 1.43553e29i | −1.47983 | + | 0.470849i | ||||
\(889\) | 2.01672e29 | 0.654076 | ||||||||
\(890\) | 1.97501e29 | + | 2.73004e29i | 0.633387 | + | 0.875526i | ||||
\(891\) | −4.81451e29 | −1.52677 | ||||||||
\(892\) | 5.02364e29 | + | 1.65493e29i | 1.57532 | + | 0.518957i | ||||
\(893\) | − | 1.69317e29i | − | 0.525031i | ||||||
\(894\) | −2.87581e29 | − | 3.97521e29i | −0.881829 | − | 1.21895i | ||||
\(895\) | − | 1.83857e29i | − | 0.557507i | ||||||
\(896\) | 4.11244e29 | + | 1.40134e29i | 1.23316 | + | 0.420207i | ||||
\(897\) | −6.93271e29 | −2.05579 | ||||||||
\(898\) | 4.45984e29 | − | 3.22640e29i | 1.30784 | − | 0.946140i | ||||
\(899\) | −3.33179e27 | −0.00966229 | ||||||||
\(900\) | −3.15692e28 | + | 9.58299e28i | −0.0905395 | + | 0.274837i | ||||
\(901\) | 5.62502e27i | 0.0159542i | ||||||||
\(902\) | 1.05387e29 | − | 7.62405e28i | 0.295611 | − | 0.213856i | ||||
\(903\) | − | 8.74970e28i | − | 0.242726i | ||||||
\(904\) | 7.66425e28 | + | 2.40880e29i | 0.210274 | + | 0.660869i | ||||
\(905\) | 3.26073e29 | 0.884768 | ||||||||
\(906\) | −4.06630e29 | − | 5.62082e29i | −1.09123 | − | 1.50841i | ||||
\(907\) | −3.26703e29 | −0.867121 | −0.433561 | − | 0.901124i | \(-0.642743\pi\) | ||||
−0.433561 | + | 0.901124i | \(0.642743\pi\) | |||||||
\(908\) | 1.33021e29 | − | 4.03791e29i | 0.349189 | − | 1.05998i | ||||
\(909\) | 9.25075e29i | 2.40181i | ||||||||
\(910\) | −4.49925e29 | − | 6.21928e29i | −1.15538 | − | 1.59708i | ||||
\(911\) | − | 6.33913e29i | − | 1.61007i | −0.593225 | − | 0.805037i | \(-0.702145\pi\) | ||
0.593225 | − | 0.805037i | \(-0.297855\pi\) | |||||||
\(912\) | 4.47887e29 | + | 3.31017e29i | 1.12518 | + | 0.831577i | ||||
\(913\) | 7.48244e29 | 1.85924 | ||||||||
\(914\) | −1.66625e29 | + | 1.20543e29i | −0.409524 | + | 0.296264i | ||||
\(915\) | 1.09151e30 | 2.65348 | ||||||||
\(916\) | 4.73156e29 | + | 1.55871e29i | 1.13776 | + | 0.374810i | ||||
\(917\) | − | 8.72506e29i | − | 2.07527i | ||||||
\(918\) | 5.06166e28 | − | 3.66179e28i | 0.119088 | − | 0.0861522i | ||||
\(919\) | 6.74333e29i | 1.56935i | 0.619909 | + | 0.784674i | \(0.287170\pi\) | ||||
−0.619909 | + | 0.784674i | \(0.712830\pi\) | |||||||
\(920\) | 1.16692e29 | + | 3.66750e29i | 0.268634 | + | 0.844290i | ||||
\(921\) | −8.57969e28 | −0.195378 | ||||||||
\(922\) | −4.23291e29 | − | 5.85112e29i | −0.953519 | − | 1.31804i | ||||
\(923\) | −1.63967e29 | −0.365375 | ||||||||
\(924\) | −1.26935e30 | − | 4.18160e29i | −2.79808 | − | 0.921771i | ||||
\(925\) | − | 5.72181e28i | − | 0.124772i | ||||||
\(926\) | −2.39121e29 | − | 3.30536e29i | −0.515832 | − | 0.713031i | ||||
\(927\) | − | 1.28599e30i | − | 2.74434i | ||||||
\(928\) | 1.23276e27 | − | 1.21050e29i | 0.00260254 | − | 0.255556i | ||||
\(929\) | −1.89758e29 | −0.396317 | −0.198159 | − | 0.980170i | \(-0.563496\pi\) | ||||
−0.198159 | + | 0.980170i | \(0.563496\pi\) | |||||||
\(930\) | −2.76919e28 | + | 2.00333e28i | −0.0572167 | + | 0.0413926i | ||||
\(931\) | −2.72863e29 | −0.557762 | ||||||||
\(932\) | 2.04884e28 | − | 6.21938e28i | 0.0414333 | − | 0.125773i | ||||
\(933\) | 1.04449e30i | 2.08972i | ||||||||
\(934\) | 6.04321e28 | − | 4.37187e28i | 0.119619 | − | 0.0865364i | ||||
\(935\) | − | 5.59430e28i | − | 0.109554i | ||||||
\(936\) | 1.43484e30 | − | 4.56535e29i | 2.78000 | − | 0.884535i | ||||
\(937\) | −4.06862e29 | −0.779921 | −0.389961 | − | 0.920832i | \(-0.627511\pi\) | ||||
−0.389961 | + | 0.920832i | \(0.627511\pi\) | |||||||
\(938\) | 6.60154e29 | + | 9.12527e29i | 1.25204 | + | 1.73068i | ||||
\(939\) | −6.46214e29 | −1.21261 | ||||||||
\(940\) | −1.18127e29 | + | 3.58582e29i | −0.219317 | + | 0.665748i | ||||
\(941\) | − | 4.79905e29i | − | 0.881575i | −0.897611 | − | 0.440788i | \(-0.854699\pi\) | ||
0.897611 | − | 0.440788i | \(-0.145301\pi\) | |||||||
\(942\) | 7.62961e29 | + | 1.05464e30i | 1.38673 | + | 1.91687i | ||||
\(943\) | 1.30184e29i | 0.234121i | ||||||||
\(944\) | −2.24704e29 | − | 1.66071e29i | −0.399845 | − | 0.295511i | ||||
\(945\) | 1.46385e30 | 2.57738 | ||||||||
\(946\) | 6.40491e28 | − | 4.63354e28i | 0.111584 | − | 0.0807238i | ||||
\(947\) | 7.45383e29 | 1.28493 | 0.642466 | − | 0.766315i | \(-0.277912\pi\) | ||||
0.642466 | + | 0.766315i | \(0.277912\pi\) | |||||||
\(948\) | −1.26246e30 | − | 4.15891e29i | −2.15345 | − | 0.709409i | ||||
\(949\) | 6.48525e29i | 1.09462i | ||||||||
\(950\) | −5.45324e28 | + | 3.94507e28i | −0.0910790 | + | 0.0658898i | ||||
\(951\) | 6.57285e29i | 1.08630i | ||||||||
\(952\) | 6.02309e28 | − | 1.91641e28i | 0.0985031 | − | 0.0313415i | ||||
\(953\) | −3.45171e29 | −0.558605 | −0.279303 | − | 0.960203i | \(-0.590103\pi\) | ||||
−0.279303 | + | 0.960203i | \(0.590103\pi\) | |||||||
\(954\) | −1.51540e29 | − | 2.09472e29i | −0.242685 | − | 0.335462i | ||||
\(955\) | −8.35012e29 | −1.32330 | ||||||||
\(956\) | 4.36976e29 | + | 1.43953e29i | 0.685297 | + | 0.225757i | ||||
\(957\) | 3.72381e29i | 0.577921i | ||||||||
\(958\) | −2.95207e29 | − | 4.08063e29i | −0.453390 | − | 0.626718i | ||||
\(959\) | 6.89289e29i | 1.04765i | ||||||||
\(960\) | −7.17602e29 | − | 1.01351e30i | −1.07937 | − | 1.52446i | ||||
\(961\) | 6.70830e29 | 0.998571 | ||||||||
\(962\) | −6.91835e29 | + | 5.00498e29i | −1.01918 | + | 0.737313i | ||||
\(963\) | −2.14760e30 | −3.13105 | ||||||||
\(964\) | −2.09462e29 | + | 6.35832e29i | −0.302228 | + | 0.917428i | ||||
\(965\) | − | 4.96993e28i | − | 0.0709704i | ||||||
\(966\) | 1.08373e30 | − | 7.84010e29i | 1.53162 | − | 1.10803i | ||||
\(967\) | 1.21661e29i | 0.170171i | 0.996374 | + | 0.0850855i | \(0.0271163\pi\) | ||||
−0.996374 | + | 0.0850855i | \(0.972884\pi\) | |||||||
\(968\) | −1.47084e29 | − | 4.62268e29i | −0.203615 | − | 0.639942i | ||||
\(969\) | 8.10233e28 | 0.111013 | ||||||||
\(970\) | −5.42735e29 | − | 7.50219e29i | −0.735987 | − | 1.01735i | ||||
\(971\) | 1.19798e30 | 1.60789 | 0.803945 | − | 0.594704i | \(-0.202731\pi\) | ||||
0.803945 | + | 0.594704i | \(0.202731\pi\) | |||||||
\(972\) | −5.01633e28 | + | 1.52274e29i | −0.0666383 | + | 0.202284i | ||||
\(973\) | 1.53576e30i | 2.01927i | ||||||||
\(974\) | −3.10760e28 | − | 4.29562e28i | −0.0404423 | − | 0.0559032i | ||||
\(975\) | 2.70340e29i | 0.348228i | ||||||||
\(976\) | −6.62231e29 | + | 8.96040e29i | −0.844328 | + | 1.14243i | ||||
\(977\) | −1.37051e29 | −0.172956 | −0.0864779 | − | 0.996254i | \(-0.527561\pi\) | ||||
−0.0864779 | + | 0.996254i | \(0.527561\pi\) | |||||||
\(978\) | 9.28119e28 | − | 6.71434e28i | 0.115935 | − | 0.0838716i | ||||
\(979\) | 1.05805e30 | 1.30821 | ||||||||
\(980\) | 5.77875e29 | + | 1.90369e29i | 0.707250 | + | 0.232989i | ||||
\(981\) | − | 2.29269e30i | − | 2.77751i | ||||||
\(982\) | −8.17732e29 | + | 5.91576e29i | −0.980610 | + | 0.709408i | ||||
\(983\) | 3.33608e28i | 0.0396005i | 0.999804 | + | 0.0198003i | \(0.00630303\pi\) | ||||
−0.999804 | + | 0.0198003i | \(0.993697\pi\) | |||||||
\(984\) | −1.27363e29 | − | 4.00287e29i | −0.149655 | − | 0.470350i | ||||
\(985\) | −3.74794e29 | −0.435944 | ||||||||
\(986\) | −1.03227e28 | − | 1.42690e28i | −0.0118857 | − | 0.0164295i | ||||
\(987\) | 1.31212e30 | 1.49555 | ||||||||
\(988\) | 9.54012e29 | + | 3.14279e29i | 1.07643 | + | 0.354606i | ||||
\(989\) | 7.91197e28i | 0.0883734i | ||||||||
\(990\) | 1.50712e30 | + | 2.08329e30i | 1.66647 | + | 2.30355i | ||||
\(991\) | 2.35405e29i | 0.257679i | 0.991665 | + | 0.128839i | \(0.0411251\pi\) | ||||
−0.991665 | + | 0.128839i | \(0.958875\pi\) | |||||||
\(992\) | 3.55285e26 | − | 3.48871e28i | 0.000385000 | − | 0.0378050i | ||||
\(993\) | −1.25555e30 | −1.34692 | ||||||||
\(994\) | 2.56315e29 | − | 1.85427e29i | 0.272214 | − | 0.196929i | ||||
\(995\) | −1.73913e29 | −0.182853 | ||||||||
\(996\) | 7.56062e29 | − | 2.29507e30i | 0.786981 | − | 2.38892i | ||||
\(997\) | 8.46981e29i | 0.872815i | 0.899749 | + | 0.436407i | \(0.143749\pi\) | ||||
−0.899749 | + | 0.436407i | \(0.856251\pi\) | |||||||
\(998\) | −4.66221e29 | + | 3.37280e29i | −0.475648 | + | 0.344101i | ||||
\(999\) | − | 1.62839e30i | − | 1.64476i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8.21.d.b.3.15 | ✓ | 18 | |
3.2 | odd | 2 | 72.21.b.b.19.4 | 18 | |||
4.3 | odd | 2 | 32.21.d.b.15.17 | 18 | |||
8.3 | odd | 2 | inner | 8.21.d.b.3.16 | yes | 18 | |
8.5 | even | 2 | 32.21.d.b.15.18 | 18 | |||
24.11 | even | 2 | 72.21.b.b.19.3 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.21.d.b.3.15 | ✓ | 18 | 1.1 | even | 1 | trivial | |
8.21.d.b.3.16 | yes | 18 | 8.3 | odd | 2 | inner | |
32.21.d.b.15.17 | 18 | 4.3 | odd | 2 | |||
32.21.d.b.15.18 | 18 | 8.5 | even | 2 | |||
72.21.b.b.19.3 | 18 | 24.11 | even | 2 | |||
72.21.b.b.19.4 | 18 | 3.2 | odd | 2 |